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STA2023 Application: Sample Data, Statistics, and the Empirical RulePurpose: 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. Then the sample data will be compared to the Empirical Rule. The information will then be analyzed in a written summary.Part 1: Random Data, Statistics, and the Empirical RuleMethods: 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.1. The data values and relevant information are posted in the course website. Use the data set (P, Q, R, S, or T) assigned to you by your instructor to complete this application.For the purpose of this application, treat the data set as if it represented a certain random variable and was a valid random sample gathered by a researcher from a normally distributed population. The sample data was actually found with an online Gaussian random number generator that creates normally distributed data values. The random number generator simulates the results of a researcher finding those values through observation or experimentation.2. Use technology (Excel, graphing calculator, etc.) to sort the sample data values from low to high. 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 5 to 10 class intervals, organize the sample data as a frequency distribution in a table. The intervals of the frequency distribution should be rounded to the tenths so that they match the data. Label this “Table 2: Frequency Distribution.”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 Table 2, 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 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 Summary1. Write an introduction to this application. Discuss the random variable and the source of the sample data. 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. The summary should be at least 150 words and be written with proper grammar and spelling. Refer to the tables and graph (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, how the frequency distribution was created, specifically referring to the intervals and class width, 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, 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, the Empirical Rule and compare the actual number of values within each category of the Empirical Rule to the number that should be there, how the Empirical Rule is related to the criteria for significantly low or high values, characteristics of the sample data such as significantly low/high values and skewness, providing support and examples. Use both the histogram and measures of center to identify whether there is skewness.Part 3: Format RequirementsInclude a title page with your name, STA2023 Application 1, 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 by itself 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 use first or second person (I, you, etc.). 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. 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. Title page, Introduction, Tables and Graph, Summary.Part 4: Grading: The application is worth up to 30 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. The format (Part 3) of the complete document submitted to the Assignments link is worth up to 10 points, based on completion of all the listed requirements.

## Answer

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#### Solution Steps

Step 1: Sort the Sample Data

To sort the sample data values from low to high, use Excel or similar software. Organize the data into a table with about 5 or 6 columns and label it “Table 1: Sorted Set of Sample Data.”

Step 2: Create a Frequency Distribution

Using 5 to 10 class intervals, organize the sample data as a frequency distribution in a table. Round the intervals to the tenths to match the data. Label this table as “Table 2: Frequency Distribution.”

Step 3: Construct a Frequency Histogram

Use Excel or similar software to construct a frequency histogram to illustrate the data. Ensure the axes have proper titles and label the graph as “Graph 1: Histogram.”

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1. A random sample of $n=20$ rows of data with two continuous variables in the columns needs to be compiled using a random number generator and saved as an Excel spreadsheet to analyze in Excel or in "My Data" in PearsonMyLab StatCrunch.2. The reason for the random data set is to ensure variation or representation of low, middle and high values of the two variables.3. An abstract then needs to be written based on the data set of $n=20$.4. Copy and paste the Excel data set of $\mathrm{n}=20$ (or StatCrunch $\mathrm{n}=20$ data set) at the bottom of the abstract written and saved in Word.5. Save the Word file with both the abstract and the data set (rows and columns).6. Type Full Name, RU ID and Date on Top of the DocumentWhen completed - upload as ONE SINGLE Word document in Canvas under Assignments entitled, "Statistics 401-H1 Final Data Analysis Part No. 1 - Assignment"1. How to compile a data set of $n=20$:2. Create a data set (random sample of at least $\mathrm{n}=20$, or can be $\mathrm{n}=30$ re: Central Limit Theorem) selected from any reliable source, with unit of analysis on the row (such as countries or baseball teams), and two variables in the column and save as Excel file.3. Use random number generator to select a data set of $n=20$ or $n=30$.See instructions below to create a random of $n=20$ or $n=30$.That is insert the number 1 as the minimum and then the maximum of the rows as the largest number in the entire data set -- the random number generator then selects a numberUse that number to select the row of data from the original data set. Copy and paste that row into an Excel spreadsheet. Repeat the procedure until 20 rows of random data are selected.

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DATA ANALYSIS REPORT #2:Detecting Relationships in Social Scientific Data ASSIGNMENT DESCRIPTIONWe are exploring social values of our classmates using through bivariate analyses. Bivariate tests assess the relationships between two different variables. Specifically, you will be asked to come up with a research question, review a set of data, find variables to test that question, describe data on both of those variables, perform a Chi-Square test or an ANOVA, and to interpret, report, and reflect on the results.TABLE OF CONTENTSI. Getting Started (page 2)II. Codebook (page 3)III. Report Requirements (page 4)IV. Example Assignment (page 7)V. Grading Rubric (9)VI. SPSS Analysis Instructions (page 10)REQUIRED MATERIALS- TEXTBOOK and NOTES from lessons #1 through #9.- Microsoft Word (or some other word processing software),- SPSS data analysis software, and- SPSS data file (STA2122 Student Data 2024.sav) posted to Canvas.SUBMISSION REQUIREMENTS1. Two documents are required: (1) The typewritten report must be saved in (.docx) format, and (2) The SPSS output file must be saved (.pdf) format.2. Documents uploaded to Canvas are considered final. Please confirm that you have uploaded the correct assignment by reviewing them in Canvas prior to the due date. If you upload something in error, immediately upload the correct document to the same location.3. Each fully composed report (i.e., all requirements are included, but may be done incorrectly) will be given the opportunity to revise and resubmit after grades are finalized and at the instructor's discretion. Partial attempts, blank, or placeholder assignments may not be eligible for revision.4. If you cannot complete the assignment by the due date, please take advantage of the grace period, or, request an Outlier Token for additional time5. Being able to think and write is power. Practice this power. This assignment is part summary, analysis, and synthesis. You are expected to use your own language throughout the entire report. Papers that use my example, include block quotations, rephrasing, and search-and-replace wording, are considered in violation of the university academic integrity policies.6. Generative Al (e.g., ChatGPT) may only be used in certain sections of this assignment. See instructions for details.

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Find the whole given the percent and corresponding amount of the whole. Round yours results to two decimal places as needed.Jessica earned $60 \%$ on an exam. If she earned 12 points, what was the total number of points possible on the exam? $\square$ pointsHow many points did she get marked off? $\square$ pointsAshley is on a road trip. So far she has traveled $27.13 \%$ of the trip which is 105 miles. How many miles is the entire trip? $\square$ milesHow many miles does she left to go? $\square$ milesMadison paid $\$ 69.33$ in sales tax on her books. The sales tax was $8.9 \%$ of the cost of the books. How much did Madison's books cost before tax? \$ $\square$How much did Madison pay for her books including tax? \$ $\square$Emily had her eye on a new tablet for school. The online store was having a sale of $25 \%$ off the original price which made the sale price of the tablet $\$ 906.75$. What was the original price of the tablet? \$ $\square$How much did Emily save? \$ $\square$

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If T: R3->R3 is a linear transformation such thatT([1;0;0])=[2;-1;0] T([0;1;0])=[4;-3;4] T=([0;0;1])=[1;-3;1] then T([-5;-4;1])=

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Concepts; What students need to know. 5.RI.10 By the end of the year, proficiently and independently read and comprehend informational text, including history/social studies, science and technological texts, in a text complexity range determined by qualitative and quantitative measures appropriate to grade 5.

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