Homework 2

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Indiana University, Bloomington *

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S301

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Statistics

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Feb 20, 2024

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K300 HW 2 Name: _Husanpreet Kaur_________ Due: Submitted via Canvas by 11:59 PM on Wednesday Total Points: 50 Goal: This homework is designed to practice using formulas in Excel, creating summary tables and statistics, and creating histograms. Note: there are several pages to this document, the Excel work is just the first step Please do not forget to answer the questions on pages 2 – 4. First, download and open the Excel workbook named K300_HW2.xlxs. This dataset contains fictional data representing the exam scores from 40 students across five different exams. Your first task is to generate easy to digest summary data for the values in this file. Complete the steps listed below and then save the updated file as a pdf so it can be submitted to Canvas. Excel Changes: 1. Create a new column after Exam 5 (E5) named “Avg” that reports the average exam score for each student, with the score rounded to two decimal places 2. Sort all of the data so that student with the highest exam average is at the top of the file and the student with the lowest exam average is at the bottom. 3. Create a results summary table that shows the three measures of central tendency as well as the high and low scores for each of the exams. Format the table so that the row and column headers are in bold, and the values in the table are all rounded to just one digit after the decimal point. Visually, the summary table should look something like this: with the Xs replaced by the correct calculated values. When you finish your updates to the Excel workbook, save it, and then convert or print the file to a .pdf as I demonstrated in our Week 1 workshop. The PDF file is what you will need to submit as a part of your homework (Canvas does not play well with Excel files). Once you have converted and saved your Excel file, answer the following questions:

4. This histogram represents scores from a recent K300 exam: Answer the following questions about this frequency distribution: (a) How would you describe the shape of this distribution? Unimodal and negatively skewed. (b) What is your estimate for the mean of this data? 75 (c) What is/are your estimate(s) for the mode(s) of this data? 90 5. Suppose that a researcher randomly selected 1,000 individuals from around the United States and timed each one of them as they ran the 100-meter dash. (a) After collecting the data from all 1000 participants, the researchers displayed the results in a histogram. Describe what you think the shape of the distribution would be using the terms we’ve talked about in class and explain (briefly) why you think it would look that way. The data would be unimodal and symmetric because when the participants are running some people may be faster than other and some may be slower, but overall, there will be a point at which most people have a similar speed/time. (b) State which measure of central tendency would you recommend for describing this data and why you chose that measure.

I would use the mode to describe this data because if we are using the data of 1000 individuals, I would want to see the time section that reoccurs the most often to see the peak in the data. 6. Below are four different histograms for the same set of data, using different bin sizes. The data are the points scored in each game of the 2014-2015 season by the Indiana Pacers (an NBA basketball team). (a) What is a typical number of points scored in a game? What bin size is most useful for making this determination? Explain your reasoning, including which measure of central tendency you considered. The bin size that would be most useful is bin size 5 because 5 is a round number but it is also smaller than 25 and 10 (which are also round numbers) which allows for the data to be seen more accurately yet not being too overly cluttered. (b) If the Pacers scored 115 points in a game, would that be an unusual outcome? In other words, how typical is it that the Pacers would score about 115 points? Explain your reasoning. This would an unusual outcome because the histograms show that the mode is seen to be somewhere between 90 and 100 (around 95) and the distance between the bar sizes of 95 and 115 is very significant as the graph has curved down a lot by the time it has reached 115. So, this leads to my conclusion that scoring 115 points would be fairly uncommon for the pacers.

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(c) Fill in the blank: If I went to a Pacers game, I would be surprised if the Pacers score less than _____ points. Explain your reasoning. The goal here is to think about what “surprising” means in the context of a histogram. Another way to ask this question is this: Based on data in these histograms, where is the boundary between what you would consider a fairly common result and one that is unlikely, but that still occurs occasionally. 80 points because in the graph it is seen that 80 has been mainly the lowest the pacers have scored with 70 being an outlier as further out from the graph and not connected to the data. The boundary of the data seems to be between 80 and 120 so I would be surprised if they scored lower than 80. (d) If you want to know whether the Pacers are more likely to score more than 95 points in a game or less than 95 points in a game, which bin size is the most useful? Explain your reasoning. Hint: look at each of the histograms and think about which of the representations makes it the easiest to accurately determine if there were more games above 95 points or more games below) I would still use bin 5 as it cover the range of the data while also making it so that the data isn’t too cluttered by using a smaller bin size or hidden by using too big of a bin size. After you have completed this worksheet, you will need to submit it along with the pdf version of your modified Excel file. To do this, click on the Submit button as you normally would for a Canvas assignment. Browse for, and select, your finished worksheet. Before you click on the “Submit Assignment” button, click on the “+ Add Another File” link. That link will let you attach a second file (your pdf file) to the assignment. Once both files are attached to the assignment, click “Submit Assignment” button. Don’t forget that it is your responsibility to make sure that you uploaded the correct (completed) files and that the upload and submission process was successful. You should always double-check your submissions using the process outlined in the Viewing Paper Feedback.pdf on the lecture’s Canvas site.

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