Category: Mathematics

  • [Solved] Solve quadratic equation

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    Let’s solve: x² + 5x + 6 = 0 Step 1: Identify values a = 1 b = 5 c = 6 Step 2: Substitute into formula x = (-5 ± √(5² − 4×1×6)) / (2×1) Step 3: Solve inside the square root 5² = 25 4×1×6 = 24 So: √(25 − 24) = √1 = 1 Step 4: Final calculation x = (-5 ± 1) / 2 Now split: x = (-5 + 1)/2 = -4/2 = -2 x =…

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    Assignment Prompt & Instructions

    Let’s solve: x² + 5x + 6 = 0

    Step 1: Identify values

    a = 1

    b = 5

    c = 6

    Step 2: Substitute into formula

    x = (-5 ± √(5² − 4×1×6)) / (2×1)

    Step 3: Solve inside the square root

    5² = 25

    4×1×6 = 24

    So: √(25 − 24) = √1 = 1

    Step 4: Final calculation

    x = (-5 ± 1) / 2

    Now split:

    x = (-5 + 1)/2 = -4/2 = -2

    x = (-5 – 1)/2 = -6/2 = -3

    ✅ Final Answer:

    x = -2 and x = -3

  • [Solved] Mathematics – Geometry help solve geometry homework

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    [>Geometry homework help](https://www.sweetstudy.com/fields/mathematics-geometry) I’m currently studying basic algebra and trying to get a clearer understanding of and how it works in different situations. To practice, I’ve created a set of questions below. I’d like a detailed, step-by-step explanat…

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    [>Geometry homework help](https://www.sweetstudy.com/fields/mathematics-geometry)

    I’m currently studying basic algebra and trying to get a clearer understanding of  and how it works in different situations. To practice, I’ve created a set of questions below. I’d like a detailed, step-by-step explanation for each part so I can learn how to solve similar problems on my own.

    ### **Part A**

    Given two points:

    A(3, −2) and B(7, 4)

    – Find the slope of the line passing through these points.
    – Clearly explain the slope formula and show each step of the calculation.
    – Describe what the slope means in this situation (for example: whether it is positive or negative, how steep the line is, and what direction it moves).

    ### **Part B**

    Now suppose point B changes position to B′(7, −2).

    – Calculate the new slope of the line connecting A(3, −2) and B′(7, −2).
    – Compare this slope to the one found in Part A.
    – Identify the type of line formed (horizontal, vertical, or diagonal) and explain your reasoning.

    ### **Part C**

    Next, consider switching the y-values of the original points:

    C(3, 4) and D(7, −2)

    – Find the slope between these two new points.
    – Compare this slope to the original slope from Part A in terms of value and direction.
    – Finally, explain what happens if both points have the same x-value (for example: C(5, 4) and D(5, −2)). What kind of line would this produce, and why?

    I’m hoping to better understand how slope behaves under different conditions and how to recognize patterns when working with linear equations.

  • [Solved] statistics

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    [>Statistics homework help](https://www.sweetstudy.com/fields/mathematics-statistics) Students will read a scholarly journal article and a non-scholarly article about a specific topic that will be provided in the course. Items to consider when reading the articles include noting the issue, methodolo…

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    Assignment Prompt & Instructions

    [>Statistics homework help](https://www.sweetstudy.com/fields/mathematics-statistics)

    Students will read a scholarly journal article and a non-scholarly article about a specific topic that will be provided in the course.  Items to consider when reading the articles include noting the issue, methodology, and results.

  • [Solved] bsn

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    [>Geometry homework help](https://www.sweetstudy.com/fields/mathematics-geometry)

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    Assignment Prompt & Instructions

    [>Geometry homework help](https://www.sweetstudy.com/fields/mathematics-geometry)

  • [Solved] math

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    – [\ \ Screenshot2026-04-15at2.03.29PM.png](https://www.sweetstudy.com/files/screenshot2026-04-15at2-03-29pm-png "Screenshot2026-04-15at2.03.29PM.png")

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    – [\
    \
    Screenshot2026-04-15at2.03.29PM.png](https://www.sweetstudy.com/files/screenshot2026-04-15at2-03-29pm-png "Screenshot2026-04-15at2.03.29PM.png")

  • [Solved] math

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    – [\ \ Screenshot2026-04-15at2.03.29PM.png](https://www.sweetstudy.com/files/screenshot2026-04-15at2-03-29pm-png-10534441 "Screenshot2026-04-15at2.03.29PM.png")

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    Assignment Prompt & Instructions

    – [\
    \
    Screenshot2026-04-15at2.03.29PM.png](https://www.sweetstudy.com/files/screenshot2026-04-15at2-03-29pm-png-10534441 "Screenshot2026-04-15at2.03.29PM.png")

  • [Solved] Understanding Slope Through Different Point Changes

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    I’m practicing coordinate geometry and trying to better understand how slope behaves when points change. I created the following multi-part problem and would really appreciate a clear, [speed stars](https://speed-stars.co/) step-by-step explanation for each part. **Part A:** Given two points E(2, 1)…

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    Assignment Prompt & Instructions

    I’m practicing coordinate geometry and trying to better understand how slope behaves when points change. I created the following multi-part problem and would really appreciate a clear, [speed stars](https://speed-stars.co/) step-by-step explanation for each part.

    **Part A:**

    Given two points E(2, 1) and F(6, 9):

    – Calculate the slope of the line passing through these points.
    – Show the formula used and explain each step clearly.
    – Describe what this slope tells us about the line (direction, steepness, increasing or decreasing).

    **Part B:**

    Now change point F to a new position F'(6, 1):

    – Find the slope of the line between E(2, 1) and F'(6, 1).
    – Compare this slope with the one from Part A.
    – Identify what type of line is formed and explain why.

    **Part C:**

    Consider two new points G(2, 9) and H(6, 1):

    – Calculate the slope between G and H.
    – Compare it with the slope from Part A in terms of sign and direction.
    – Explain what happens if both points have the same x-coordinate (for example, G(4, 9) and H(4, 1)). What kind of line is formed in that case?

  • [Solved] Help with Math Intervention Analysis

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    **files (2)** – ## Meta-AnalysisonMathInterventionsAssignmentInstructions2.docx – Gersten-MathematicsInstructionStudents-2009.pdf **## Meta-AnalysisonMathInterventionsAssignmentInstructions2.docx** EDLC 530 **Meta-Analysis on Math Interventions Assignment Instructions** Located in the Learn section …

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    Assignment Prompt & Instructions

    **files (2)**

    – ## Meta-AnalysisonMathInterventionsAssignmentInstructions2.docx

    – Gersten-MathematicsInstructionStudents-2009.pdf

    **## Meta-AnalysisonMathInterventionsAssignmentInstructions2.docx**

    EDLC 530

    **Meta-Analysis on Math Interventions Assignment Instructions**

    Located in the Learn section of Module 2: Week 2, you will find the
    **Read: Mathematics Instruction for Students with Learning Disabilities: A Meta-Analysis of Instructional Components** item. Please review this article and provide the following in a current APA style paper with the following section headings:

    **Summary:** Key points are concisely summarized with balance, clarity, and relevance. Evidence-based interventions are identified.

    **Analysis:** Relevant and legitimate information clearly supports the critique. It is a thoughtful, focused, in-depth analysis of the topic. Interventions are explained and evidence for their usage is discussed.

    **Application:** The information learned is applied appropriately and with insight for future use.

    It is expected that after completing this assignment you will be able to determine possible interventions for students identified as learning disabled in mathematics, how those interventions are best employed and what the expected outcomes should be from their usage. The current APA-style paper should be at least 3 pages in length, not including the title page and the references page.

    Note: Your assignment will be checked for originality via the Turnitin plagiarism tool.

    **Gersten-MathematicsInstructionStudents-2009.pdf**

    This file is too large to display. [View in new window](https://www.sweetstudy.com/files/gersten-mathematicsinstructionstudents-2009-pdf)

    **Gersten-MathematicsInstructionStudents-2009.pdf**

    This file is too large to display. [View in new window](https://www.sweetstudy.com/files/gersten-mathematicsinstructionstudents-2009-pdf)

    **## Meta-AnalysisonMathInterventionsAssignmentInstructions2.docx**

    EDLC 530

    **Meta-Analysis on Math Interventions Assignment Instructions**

    Located in the Learn section of Module 2: Week 2, you will find the
    **Read: Mathematics Instruction for Students with Learning Disabilities: A Meta-Analysis of Instructional Components** item. Please review this article and provide the following in a current APA style paper with the following section headings:

    **Summary:** Key points are concisely summarized with balance, clarity, and relevance. Evidence-based interventions are identified.

    **Analysis:** Relevant and legitimate information clearly supports the critique. It is a thoughtful, focused, in-depth analysis of the topic. Interventions are explained and evidence for their usage is discussed.

    **Application:** The information learned is applied appropriately and with insight for future use.

    It is expected that after completing this assignment you will be able to determine possible interventions for students identified as learning disabled in mathematics, how those interventions are best employed and what the expected outcomes should be from their usage. The current APA-style paper should be at least 3 pages in length, not including the title page and the references page.

    Note: Your assignment will be checked for originality via the Turnitin plagiarism tool.

    **Gersten-MathematicsInstructionStudents-2009.pdf**

    This file is too large to display. [View in new window](https://www.sweetstudy.com/files/gersten-mathematicsinstructionstudents-2009-pdf)

    **## Meta-AnalysisonMathInterventionsAssignmentInstructions2.docx**

    EDLC 530

    **Meta-Analysis on Math Interventions Assignment Instructions**

    Located in the Learn section of Module 2: Week 2, you will find the
    **Read: Mathematics Instruction for Students with Learning Disabilities: A Meta-Analysis of Instructional Components** item. Please review this article and provide the following in a current APA style paper with the following section headings:

    **Summary:** Key points are concisely summarized with balance, clarity, and relevance. Evidence-based interventions are identified.

    **Analysis:** Relevant and legitimate information clearly supports the critique. It is a thoughtful, focused, in-depth analysis of the topic. Interventions are explained and evidence for their usage is discussed.

    **Application:** The information learned is applied appropriately and with insight for future use.

    It is expected that after completing this assignment you will be able to determine possible interventions for students identified as learning disabled in mathematics, how those interventions are best employed and what the expected outcomes should be from their usage. The current APA-style paper should be at least 3 pages in length, not including the title page and the references page.

    Note: Your assignment will be checked for originality via the Turnitin plagiarism tool.

    **Gersten-MathematicsInstructionStudents-2009.pdf**

    This file is too large to display. [View in new window](https://www.sweetstudy.com/files/gersten-mathematicsinstructionstudents-2009-pdf)

  • [Solved] Application

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    [>Statistics homework help](https://www.sweetstudy.com/fields/mathematics-statistics) **files (5)** – ## Document19.docx – ## Templatefortable5.docx – ## ApplicationInstructionssaylor2026.pdf – STA2023ExampleApplication2018.docx – STA2023-newdata-2026.docx **## Document19.docx** Please click on the …

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    Have this question answered from scratch according to your specific instructions and deadline.

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    Assignment Prompt & Instructions

    [>Statistics homework help](https://www.sweetstudy.com/fields/mathematics-statistics)

    **files (5)**

    – ## Document19.docx

    – ## Templatefortable5.docx

    – ## ApplicationInstructionssaylor2026.pdf

    – STA2023ExampleApplication2018.docx
    – STA2023-newdata-2026.docx

    **## Document19.docx**

    Please click on the following links to find the instructions and necessary data for your Application:

    1. Here are the
    [Application Instructions](https://class.daytonastate.edu/d2l/common/dialogs/quickLink/quickLink.d2l?ou=503691&type=coursefile&fileId=my+stuff+and+appl+files+sp26%2fApplication+Instructions+(saylor2026).pdf)

    2. Here are the data sets
    [STA2023 Application Data Sets](https://class.daytonastate.edu/d2l/common/dialogs/quickLink/quickLink.d2l?ou=503691&type=coursefile&fileId=my+stuff+and+appl+files+sp26%2fSTA2023-newdata-2026.docx) and
    [Template for table 5](https://class.daytonastate.edu/d2l/common/dialogs/quickLink/quickLink.d2l?ou=503691&type=coursefile&fileId=Application+Files%2fTemplate+for+table+5.docx). Choose one of the 4 data sets for your application, being certain to state which data set is used in your finished application (see instructions). You will use the data values for your calculations and the table template to help you insert the correct statistical symbols in your final document.

    3. Here is an
    [Example Submission](https://class.daytonastate.edu/d2l/common/dialogs/quickLink/quickLink.d2l?ou=503691&type=coursefile&fileId=Application+Files%2fSTA2023ExampleApplication2018.docx) to help you with what I am looking for in terms of formatting you document.

    Here are some videos that will help you create your tables and histogram:

    ·
    [Creating Tables in Excel](https://www.youtube.com/watch?v=477EbiiBHR8&feature=youtu.be)

    ·
    [Creating a Histogram](https://www.youtube.com/watch?v=DfBkqIWemMs&feature=youtu.be)

    Please let me know if you have any questions! You can also post on the
    [Application Forum](https://class.daytonastate.edu/d2l/common/dialogs/quickLink/quickLink.d2l?ou=503691&type=discuss&rcode=DBC-1571919) under discussions to get help from me and your classmates on the Application.

    **## Templatefortable5.docx**

    Template for table 5

    | | | | | |
    | — | — | — | — | — |
    | Sample size: n=48 |
    | Category of Empirical Rule | number of data values which should be within cut off values | lower cut-off | upper cut-off | number of data values which actually are within cut-off values |
    | 68% | 33 | – s = 30.31 | + s = 37.85 | 30 |
    | 95% | 46 | – 2s = 26.54 | + 2s = 41.26 | 45 |
    | 99.70% | 48 | – 3s = 22.77 | + 3s = 45.39 | 48 |

    Table 5: The Empirical Rule

    **## ApplicationInstructionssaylor2026.pdf**

    STA2023 Application (2026) 1

    STA2023 Application: Sample Data, Statistics, and the Empirical Rule

    The completed application should be submitted to the Assignments link in Falcon Online.

    Purpose: The purpose of this assignment is to organize a random sample of data values and create
    statistics, tables, and a graph based on the data. This will help you apply what you have learned to a
    real-world variable. Then the sample data will be compared to the Empirical Rule. The information will
    then be analyzed in a written summary.

    READ THIS ENTIRE DOCUMENT BEFORE STARTING THE APPLICATION ASSIGNMENT.

    Part 1: Random Data, Statistics, and the Empirical Rule

    How to Complete the Assignment: Use Excel (or similar software) to create the tables and graph. Then
    copy the items and paste them into a Word document. The tables should be formatted vertically, have
    borders, and be given the labels and titles stated in the assignment. The proper symbols should be used.
    Do not submit this assignment as an Excel file. The completed assignment should be a Word (or .pdf)
    document. In addition to your tables and graphs, include the written introduction and summary in the
    Word document.

    1. The data values and relevant information are posted in the Assignment link in Falcon Online. Use one
    of the 4 data sets to complete this application.

    When you are discussing the data set in your application introduction and summary, use the relevant
    information provided with the data set. The random variable x is defined for each data set. This will
    allow you to discuss the statistics in a meaningful way.

    2. Use technology (Excel, graphing calculator, etc.) to sort the sample data values from smallest to
    largest. Use Excel or similar software to put the data into a table with about 5 or 6 columns. Label this
    “Table 1: Sorted Set of Sample Data.”

    3. Using 8 class intervals, organize the sample data as a frequency distribution in a table. Guidelines on
    creating a frequency distribution can be found in your textbook in Section 2.1. Label this “Table 2:
    Frequency Distribution.” Be certain to use an integer value for the class width. Start the first interval
    with a whole number just less than the minimum value of the data set. The lower and upper class limits
    of the intervals should be rounded to the tenths like the data values.

    4. Use Excel (or similar software) to construct a frequency histogram to illustrate the data. Give the axes
    the proper titles. Label this “Graph 1: Histogram.”

    5. Use the frequency distribution to find the midpoints of each class interval. Create a new frequency
    distribution with the midpoints in the left column and the frequencies in the right column. Label this
    “Table 3: Frequency Distribution with Midpoints.”

    6. Use technology to find the mean, median, standard deviation, and variance of the sample data
    organized in Table 3 (from step 5 above). Put these values into a table with the proper symbol in the left
    column and the value of the statistic in the right column. Also, from the original data set, put the values
    of the range and sample size in the table. The median and range do not generally have symbols so the

    STA2023 Application (2026) 2

    terms “Median” and “Range” can be used in the left column. Identify the modal class (the one with the
    highest frequency). Put the terms “Modal Class” in the left column and the class interval in the right
    column. The statistics should be rounded properly (one more decimal place than the data). Label this
    “Table 4: Summary Statistics”

    7. Use the sample mean and standard deviation to find the values related to the Empirical Rule.
    The Empirical Rule: For a set of data whose distribution is approximately normal,

    • about 68% of the data are within one standard deviation of the mean.

    • about 95% of the data are within two standard deviations of the mean.

    • about 99.7% of the data are within three standard deviations of the mean.

    Use the value of n and the percents listed above to find how many data values should be within each
    category. Then use the sample mean and standard deviation to find the lower and upper cut-off values
    in each category. Then use the sorted list of data to determine how many values are actually in each
    category. Put the values into a table as shown in the example and label it “Table 5: The Empirical Rule.”

    Part 2: Written Introduction and Summary

    1. Write an introduction to this application. Discuss the random variable for the data set. Refer to the
    textbook or class notes to describe the basic components of the application and the statistical concepts
    that are applied. The introduction should be at least 50 words and be written with proper grammar and
    spelling.

    2. Write a summary of the application, considering the following topics listed below. The summary
    should be at least 150 words and be written with proper grammar and spelling. Refer to the tables and
    graph you created (by label and number) throughout the summary. Use the proper statistical terms and
    symbols in the summary. Write about the concepts in the application rather than the steps followed. Do
    not number the parts or steps in the application except for the proper numbering of the tables and
    graph.

    • Discuss the difference between population and sample values.

    • Discuss how the frequency distribution was created, specifically referring to the intervals and
    class width.

    • Describe the features of the histogram, including the axes and the shape of the distribution,
    especially whether it meets the criteria of an approximately normal distribution.

    • Discuss measures of center and variation as related to the sample data; given the values used in
    the random number generator, compare the sample values to those of the population.

    • Discuss the Empirical Rule and compare the actual number of values within each category of the
    Empirical Rule to the number that should be there.

    • Discuss how the Empirical Rule is related to the criteria for unusual values.

    • Discuss characteristics of the sample data such as unusual values, outliers, and skewness,
    providing support and examples. Use both the histogram and measures of center to identify
    whether there is skewness.

    STA2023 Application (2026) 3

    Part 3: Format Requirements

    • Include a title page with your name, STA2023 Application, the word count for the introduction,
    the word count for the summary, and which data set is used.

    • The introduction and summary should be written in paragraphs that are typed and double-
    spaced, with 1-inch margins and a readable font type and font size. The preferred font size could
    be 12 Times New Roman.

    • The introduction should be at least 50 words.

    • The summary should be at least 150 words.

    • The introduction and summary should be college-level writing with proper grammar and
    spelling.

    • Do not write about the parts of the assignment or the use of a calculator or excel to complete
    steps in the application. Write about the concepts used in the application and what the
    calculations and graphs tell you about the data.

    • Throughout the introduction, tables, graph, and summary, proper statistical symbols and terms
    should be used.

    • The tables should be formatted vertically, have 2 columns (unless specified otherwise), have
    borders, and be given the labels and titles stated in the assignment.

    • The title page, introduction, tables, graphs, and summary should be a single document (.doc,
    .docx, or .pdf) which is submitted to the Assignments link in Falcon Online by the due date.

    • Assemble the application in the following order to create a single document.
    o Title page
    o Introduction
    o Tables and Graph
    o Summary

    Part 4: Grading
    The application is worth up to 20 points, based on the following criteria.

    • The statistical content (Part 1) is worth up to 10 points, based on completion of all the listed
    requirements.

    • The introduction and written summary (Part 2) are worth up to 10 points, based on completion
    of all the listed requirements.

    Rubric/allocation of 10 points:

    • 0 points for completing none of the requirements

    • 2 points for attempting the requirements

    • 4 points for completing some of the requirements

    • 8 points for completing most of the requirements

    • 10 points for completing all of the requirements

    **STA2023ExampleApplication2018.docx**

    This file is too large to display. [View in new window](https://www.sweetstudy.com/files/sta2023exampleapplication2018-docx-10537337)

    **STA2023-newdata-2026.docx**

    This file is too large to display. [View in new window](https://www.sweetstudy.com/files/sta2023-newdata-2026-docx)

    **STA2023-newdata-2026.docx**

    This file is too large to display. [View in new window](https://www.sweetstudy.com/files/sta2023-newdata-2026-docx)

    **## Document19.docx**

    Please click on the following links to find the instructions and necessary data for your Application:

    1. Here are the
    [Application Instructions](https://class.daytonastate.edu/d2l/common/dialogs/quickLink/quickLink.d2l?ou=503691&type=coursefile&fileId=my+stuff+and+appl+files+sp26%2fApplication+Instructions+(saylor2026).pdf)

    2. Here are the data sets
    [STA2023 Application Data Sets](https://class.daytonastate.edu/d2l/common/dialogs/quickLink/quickLink.d2l?ou=503691&type=coursefile&fileId=my+stuff+and+appl+files+sp26%2fSTA2023-newdata-2026.docx) and
    [Template for table 5](https://class.daytonastate.edu/d2l/common/dialogs/quickLink/quickLink.d2l?ou=503691&type=coursefile&fileId=Application+Files%2fTemplate+for+table+5.docx). Choose one of the 4 data sets for your application, being certain to state which data set is used in your finished application (see instructions). You will use the data values for your calculations and the table template to help you insert the correct statistical symbols in your final document.

    3. Here is an
    [Example Submission](https://class.daytonastate.edu/d2l/common/dialogs/quickLink/quickLink.d2l?ou=503691&type=coursefile&fileId=Application+Files%2fSTA2023ExampleApplication2018.docx) to help you with what I am looking for in terms of formatting you document.

    Here are some videos that will help you create your tables and histogram:

    ·
    [Creating Tables in Excel](https://www.youtube.com/watch?v=477EbiiBHR8&feature=youtu.be)

    ·
    [Creating a Histogram](https://www.youtube.com/watch?v=DfBkqIWemMs&feature=youtu.be)

    Please let me know if you have any questions! You can also post on the
    [Application Forum](https://class.daytonastate.edu/d2l/common/dialogs/quickLink/quickLink.d2l?ou=503691&type=discuss&rcode=DBC-1571919) under discussions to get help from me and your classmates on the Application.

    **## Templatefortable5.docx**

    Template for table 5

    | | | | | |
    | — | — | — | — | — |
    | Sample size: n=48 |
    | Category of Empirical Rule | number of data values which should be within cut off values | lower cut-off | upper cut-off | number of data values which actually are within cut-off values |
    | 68% | 33 | – s = 30.31 | + s = 37.85 | 30 |
    | 95% | 46 | – 2s = 26.54 | + 2s = 41.26 | 45 |
    | 99.70% | 48 | – 3s = 22.77 | + 3s = 45.39 | 48 |

    Table 5: The Empirical Rule

    **## ApplicationInstructionssaylor2026.pdf**

    STA2023 Application (2026) 1

    STA2023 Application: Sample Data, Statistics, and the Empirical Rule

    The completed application should be submitted to the Assignments link in Falcon Online.

    Purpose: The purpose of this assignment is to organize a random sample of data values and create
    statistics, tables, and a graph based on the data. This will help you apply what you have learned to a
    real-world variable. Then the sample data will be compared to the Empirical Rule. The information will
    then be analyzed in a written summary.

    READ THIS ENTIRE DOCUMENT BEFORE STARTING THE APPLICATION ASSIGNMENT.

    Part 1: Random Data, Statistics, and the Empirical Rule

    How to Complete the Assignment: Use Excel (or similar software) to create the tables and graph. Then
    copy the items and paste them into a Word document. The tables should be formatted vertically, have
    borders, and be given the labels and titles stated in the assignment. The proper symbols should be used.
    Do not submit this assignment as an Excel file. The completed assignment should be a Word (or .pdf)
    document. In addition to your tables and graphs, include the written introduction and summary in the
    Word document.

    1. The data values and relevant information are posted in the Assignment link in Falcon Online. Use one
    of the 4 data sets to complete this application.

    When you are discussing the data set in your application introduction and summary, use the relevant
    information provided with the data set. The random variable x is defined for each data set. This will
    allow you to discuss the statistics in a meaningful way.

    2. Use technology (Excel, graphing calculator, etc.) to sort the sample data values from smallest to
    largest. Use Excel or similar software to put the data into a table with about 5 or 6 columns. Label this
    “Table 1: Sorted Set of Sample Data.”

    3. Using 8 class intervals, organize the sample data as a frequency distribution in a table. Guidelines on
    creating a frequency distribution can be found in your textbook in Section 2.1. Label this “Table 2:
    Frequency Distribution.” Be certain to use an integer value for the class width. Start the first interval
    with a whole number just less than the minimum value of the data set. The lower and upper class limits
    of the intervals should be rounded to the tenths like the data values.

    4. Use Excel (or similar software) to construct a frequency histogram to illustrate the data. Give the axes
    the proper titles. Label this “Graph 1: Histogram.”

    5. Use the frequency distribution to find the midpoints of each class interval. Create a new frequency
    distribution with the midpoints in the left column and the frequencies in the right column. Label this
    “Table 3: Frequency Distribution with Midpoints.”

    6. Use technology to find the mean, median, standard deviation, and variance of the sample data
    organized in Table 3 (from step 5 above). Put these values into a table with the proper symbol in the left
    column and the value of the statistic in the right column. Also, from the original data set, put the values
    of the range and sample size in the table. The median and range do not generally have symbols so the

    STA2023 Application (2026) 2

    terms “Median” and “Range” can be used in the left column. Identify the modal class (the one with the
    highest frequency). Put the terms “Modal Class” in the left column and the class interval in the right
    column. The statistics should be rounded properly (one more decimal place than the data). Label this
    “Table 4: Summary Statistics”

    7. Use the sample mean and standard deviation to find the values related to the Empirical Rule.
    The Empirical Rule: For a set of data whose distribution is approximately normal,

    • about 68% of the data are within one standard deviation of the mean.

    • about 95% of the data are within two standard deviations of the mean.

    • about 99.7% of the data are within three standard deviations of the mean.

    Use the value of n and the percents listed above to find how many data values should be within each
    category. Then use the sample mean and standard deviation to find the lower and upper cut-off values
    in each category. Then use the sorted list of data to determine how many values are actually in each
    category. Put the values into a table as shown in the example and label it “Table 5: The Empirical Rule.”

    Part 2: Written Introduction and Summary

    1. Write an introduction to this application. Discuss the random variable for the data set. Refer to the
    textbook or class notes to describe the basic components of the application and the statistical concepts
    that are applied. The introduction should be at least 50 words and be written with proper grammar and
    spelling.

    2. Write a summary of the application, considering the following topics listed below. The summary
    should be at least 150 words and be written with proper grammar and spelling. Refer to the tables and
    graph you created (by label and number) throughout the summary. Use the proper statistical terms and
    symbols in the summary. Write about the concepts in the application rather than the steps followed. Do
    not number the parts or steps in the application except for the proper numbering of the tables and
    graph.

    • Discuss the difference between population and sample values.

    • Discuss how the frequency distribution was created, specifically referring to the intervals and
    class width.

    • Describe the features of the histogram, including the axes and the shape of the distribution,
    especially whether it meets the criteria of an approximately normal distribution.

    • Discuss measures of center and variation as related to the sample data; given the values used in
    the random number generator, compare the sample values to those of the population.

    • Discuss the Empirical Rule and compare the actual number of values within each category of the
    Empirical Rule to the number that should be there.

    • Discuss how the Empirical Rule is related to the criteria for unusual values.

    • Discuss characteristics of the sample data such as unusual values, outliers, and skewness,
    providing support and examples. Use both the histogram and measures of center to identify
    whether there is skewness.

    STA2023 Application (2026) 3

    Part 3: Format Requirements

    • Include a title page with your name, STA2023 Application, the word count for the introduction,
    the word count for the summary, and which data set is used.

    • The introduction and summary should be written in paragraphs that are typed and double-
    spaced, with 1-inch margins and a readable font type and font size. The preferred font size could
    be 12 Times New Roman.

    • The introduction should be at least 50 words.

    • The summary should be at least 150 words.

    • The introduction and summary should be college-level writing with proper grammar and
    spelling.

    • Do not write about the parts of the assignment or the use of a calculator or excel to complete
    steps in the application. Write about the concepts used in the application and what the
    calculations and graphs tell you about the data.

    • Throughout the introduction, tables, graph, and summary, proper statistical symbols and terms
    should be used.

    • The tables should be formatted vertically, have 2 columns (unless specified otherwise), have
    borders, and be given the labels and titles stated in the assignment.

    • The title page, introduction, tables, graphs, and summary should be a single document (.doc,
    .docx, or .pdf) which is submitted to the Assignments link in Falcon Online by the due date.

    • Assemble the application in the following order to create a single document.
    o Title page
    o Introduction
    o Tables and Graph
    o Summary

    Part 4: Grading
    The application is worth up to 20 points, based on the following criteria.

    • The statistical content (Part 1) is worth up to 10 points, based on completion of all the listed
    requirements.

    • The introduction and written summary (Part 2) are worth up to 10 points, based on completion
    of all the listed requirements.

    Rubric/allocation of 10 points:

    • 0 points for completing none of the requirements

    • 2 points for attempting the requirements

    • 4 points for completing some of the requirements

    • 8 points for completing most of the requirements

    • 10 points for completing all of the requirements

    **STA2023ExampleApplication2018.docx**

    This file is too large to display. [View in new window](https://www.sweetstudy.com/files/sta2023exampleapplication2018-docx-10537337)

    **STA2023-newdata-2026.docx**

    This file is too large to display. [View in new window](https://www.sweetstudy.com/files/sta2023-newdata-2026-docx)

    **## Document19.docx**

    Please click on the following links to find the instructions and necessary data for your Application:

    1. Here are the
    [Application Instructions](https://class.daytonastate.edu/d2l/common/dialogs/quickLink/quickLink.d2l?ou=503691&type=coursefile&fileId=my+stuff+and+appl+files+sp26%2fApplication+Instructions+(saylor2026).pdf)

    2. Here are the data sets
    [STA2023 Application Data Sets](https://class.daytonastate.edu/d2l/common/dialogs/quickLink/quickLink.d2l?ou=503691&type=coursefile&fileId=my+stuff+and+appl+files+sp26%2fSTA2023-newdata-2026.docx) and
    [Template for table 5](https://class.daytonastate.edu/d2l/common/dialogs/quickLink/quickLink.d2l?ou=503691&type=coursefile&fileId=Application+Files%2fTemplate+for+table+5.docx). Choose one of the 4 data sets for your application, being certain to state which data set is used in your finished application (see instructions). You will use the data values for your calculations and the table template to help you insert the correct statistical symbols in your final document.

    3. Here is an
    [Example Submission](https://class.daytonastate.edu/d2l/common/dialogs/quickLink/quickLink.d2l?ou=503691&type=coursefile&fileId=Application+Files%2fSTA2023ExampleApplication2018.docx) to help you with what I am looking for in terms of formatting you document.

    Here are some videos that will help you create your tables and histogram:

    ·
    [Creating Tables in Excel](https://www.youtube.com/watch?v=477EbiiBHR8&feature=youtu.be)

    ·
    [Creating a Histogram](https://www.youtube.com/watch?v=DfBkqIWemMs&feature=youtu.be)

    Please let me know if you have any questions! You can also post on the
    [Application Forum](https://class.daytonastate.edu/d2l/common/dialogs/quickLink/quickLink.d2l?ou=503691&type=discuss&rcode=DBC-1571919) under discussions to get help from me and your classmates on the Application.

    **## Templatefortable5.docx**

    Template for table 5

    | | | | | |
    | — | — | — | — | — |
    | Sample size: n=48 |
    | Category of Empirical Rule | number of data values which should be within cut off values | lower cut-off | upper cut-off | number of data values which actually are within cut-off values |
    | 68% | 33 | – s = 30.31 | + s = 37.85 | 30 |
    | 95% | 46 | – 2s = 26.54 | + 2s = 41.26 | 45 |
    | 99.70% | 48 | – 3s = 22.77 | + 3s = 45.39 | 48 |

    Table 5: The Empirical Rule

    **## ApplicationInstructionssaylor2026.pdf**

    STA2023 Application (2026) 1

    STA2023 Application: Sample Data, Statistics, and the Empirical Rule

    The completed application should be submitted to the Assignments link in Falcon Online.

    Purpose: The purpose of this assignment is to organize a random sample of data values and create
    statistics, tables, and a graph based on the data. This will help you apply what you have learned to a
    real-world variable. Then the sample data will be compared to the Empirical Rule. The information will
    then be analyzed in a written summary.

    READ THIS ENTIRE DOCUMENT BEFORE STARTING THE APPLICATION ASSIGNMENT.

    Part 1: Random Data, Statistics, and the Empirical Rule

    How to Complete the Assignment: Use Excel (or similar software) to create the tables and graph. Then
    copy the items and paste them into a Word document. The tables should be formatted vertically, have
    borders, and be given the labels and titles stated in the assignment. The proper symbols should be used.
    Do not submit this assignment as an Excel file. The completed assignment should be a Word (or .pdf)
    document. In addition to your tables and graphs, include the written introduction and summary in the
    Word document.

    1. The data values and relevant information are posted in the Assignment link in Falcon Online. Use one
    of the 4 data sets to complete this application.

    When you are discussing the data set in your application introduction and summary, use the relevant
    information provided with the data set. The random variable x is defined for each data set. This will
    allow you to discuss the statistics in a meaningful way.

    2. Use technology (Excel, graphing calculator, etc.) to sort the sample data values from smallest to
    largest. Use Excel or similar software to put the data into a table with about 5 or 6 columns. Label this
    “Table 1: Sorted Set of Sample Data.”

    3. Using 8 class intervals, organize the sample data as a frequency distribution in a table. Guidelines on
    creating a frequency distribution can be found in your textbook in Section 2.1. Label this “Table 2:
    Frequency Distribution.” Be certain to use an integer value for the class width. Start the first interval
    with a whole number just less than the minimum value of the data set. The lower and upper class limits
    of the intervals should be rounded to the tenths like the data values.

    4. Use Excel (or similar software) to construct a frequency histogram to illustrate the data. Give the axes
    the proper titles. Label this “Graph 1: Histogram.”

    5. Use the frequency distribution to find the midpoints of each class interval. Create a new frequency
    distribution with the midpoints in the left column and the frequencies in the right column. Label this
    “Table 3: Frequency Distribution with Midpoints.”

    6. Use technology to find the mean, median, standard deviation, and variance of the sample data
    organized in Table 3 (from step 5 above). Put these values into a table with the proper symbol in the left
    column and the value of the statistic in the right column. Also, from the original data set, put the values
    of the range and sample size in the table. The median and range do not generally have symbols so the

    STA2023 Application (2026) 2

    terms “Median” and “Range” can be used in the left column. Identify the modal class (the one with the
    highest frequency). Put the terms “Modal Class” in the left column and the class interval in the right
    column. The statistics should be rounded properly (one more decimal place than the data). Label this
    “Table 4: Summary Statistics”

    7. Use the sample mean and standard deviation to find the values related to the Empirical Rule.
    The Empirical Rule: For a set of data whose distribution is approximately normal,

    • about 68% of the data are within one standard deviation of the mean.

    • about 95% of the data are within two standard deviations of the mean.

    • about 99.7% of the data are within three standard deviations of the mean.

    Use the value of n and the percents listed above to find how many data values should be within each
    category. Then use the sample mean and standard deviation to find the lower and upper cut-off values
    in each category. Then use the sorted list of data to determine how many values are actually in each
    category. Put the values into a table as shown in the example and label it “Table 5: The Empirical Rule.”

    Part 2: Written Introduction and Summary

    1. Write an introduction to this application. Discuss the random variable for the data set. Refer to the
    textbook or class notes to describe the basic components of the application and the statistical concepts
    that are applied. The introduction should be at least 50 words and be written with proper grammar and
    spelling.

    2. Write a summary of the application, considering the following topics listed below. The summary
    should be at least 150 words and be written with proper grammar and spelling. Refer to the tables and
    graph you created (by label and number) throughout the summary. Use the proper statistical terms and
    symbols in the summary. Write about the concepts in the application rather than the steps followed. Do
    not number the parts or steps in the application except for the proper numbering of the tables and
    graph.

    • Discuss the difference between population and sample values.

    • Discuss how the frequency distribution was created, specifically referring to the intervals and
    class width.

    • Describe the features of the histogram, including the axes and the shape of the distribution,
    especially whether it meets the criteria of an approximately normal distribution.

    • Discuss measures of center and variation as related to the sample data; given the values used in
    the random number generator, compare the sample values to those of the population.

    • Discuss the Empirical Rule and compare the actual number of values within each category of the
    Empirical Rule to the number that should be there.

    • Discuss how the Empirical Rule is related to the criteria for unusual values.

    • Discuss characteristics of the sample data such as unusual values, outliers, and skewness,
    providing support and examples. Use both the histogram and measures of center to identify
    whether there is skewness.

    STA2023 Application (2026) 3

    Part 3: Format Requirements

    • Include a title page with your name, STA2023 Application, the word count for the introduction,
    the word count for the summary, and which data set is used.

    • The introduction and summary should be written in paragraphs that are typed and double-
    spaced, with 1-inch margins and a readable font type and font size. The preferred font size could
    be 12 Times New Roman.

    • The introduction should be at least 50 words.

    • The summary should be at least 150 words.

    • The introduction and summary should be college-level writing with proper grammar and
    spelling.

    • Do not write about the parts of the assignment or the use of a calculator or excel to complete
    steps in the application. Write about the concepts used in the application and what the
    calculations and graphs tell you about the data.

    • Throughout the introduction, tables, graph, and summary, proper statistical symbols and terms
    should be used.

    • The tables should be formatted vertically, have 2 columns (unless specified otherwise), have
    borders, and be given the labels and titles stated in the assignment.

    • The title page, introduction, tables, graphs, and summary should be a single document (.doc,
    .docx, or .pdf) which is submitted to the Assignments link in Falcon Online by the due date.

    • Assemble the application in the following order to create a single document.
    o Title page
    o Introduction
    o Tables and Graph
    o Summary

    Part 4: Grading
    The application is worth up to 20 points, based on the following criteria.

    • The statistical content (Part 1) is worth up to 10 points, based on completion of all the listed
    requirements.

    • The introduction and written summary (Part 2) are worth up to 10 points, based on completion
    of all the listed requirements.

    Rubric/allocation of 10 points:

    • 0 points for completing none of the requirements

    • 2 points for attempting the requirements

    • 4 points for completing some of the requirements

    • 8 points for completing most of the requirements

    • 10 points for completing all of the requirements

    **STA2023ExampleApplication2018.docx**

    This file is too large to display. [View in new window](https://www.sweetstudy.com/files/sta2023exampleapplication2018-docx-10537337)

    **STA2023-newdata-2026.docx**

    This file is too large to display. [View in new window](https://www.sweetstudy.com/files/sta2023-newdata-2026-docx)

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