1 Summary Statistics Excel Tutorial Using Excel to calculate descriptive statistics Prepared for SSAC by *David McAvity – The Evergreen State College* © The Washington Center for Improving the Quality of Undergraduate Education. All rights reserved. *2007* Supporting Quantitative concepts and skills Visual Display of Data – Bar Charts Core Quantitative concepts and skills Statistics: Mean, Mode, Median and Standard Deviation

2 We’ll use this example about the number of children in the families of a class of 80 to illustrate how to use Excel to calculate a variety of descriptive statistics. The data has been grouped into a frequency table, where the values, x, are the number of children in a family, and the frequency,f, is the number of people who have families of that size. Number of Children in the Family Create a worksheet like this one and enter the data as shown in yellow cells. Use the Sum() function in the peach cell to add up the frequency column to find the total number of people in the class. This is called the population size, N. = cell with a number in it = cell with a formula in it Hint: to sum a column click in the cell you want the sum to be in (eg B13) and type =Sum(). Inside the parentheses type the cell range (in this case B4:B12). The entry would look like this: Instead of typing a cell range you can also just select the cells you want with the mouse.

3 Graphing the Solution To get a visual impression of the data it is useful to plot it. You can create a bar chart or pie chart readily in Excel. Create the following bar chart using the chart wizard. Make sure you label all the axes. To create a bar chart select the frequency column and click on the chart wizard icon. Choose the column chart type then click next. In the next dialogue box click the series tab and then fill in the correct range of values in the category (X) axis labels. Click next and then enter axis and title labels

4 Now we use Excel to assist with calculating the three measures of central tendency, the mode, median and mean. The mode is the most common value, the median is the middle value of ranked data and the mean is the sum of the values divided by the total number of values: Measures of Central Tendency Write Excel formulas in the peach colored cells in order to help you evaluate the mean, mode and median. Write down or calculate each of those statistics in separate cells of your worksheet. ( You should get a mean of 2.85) Hint: Need help with entering formulas? Here is an example: If you have a number in Cell B2 and you want to calculate the square of it in Cell C2 then in C2 you type =B2^2. If you have another value in B3 then if you copy cell C2 to C3 the formula will update to reference C3. This is called a relative reference. If you want the formula to always refer to a particular cell (eg B2) use an absolute reference: type =$B$2^2 instead. This column is the cumulative sum of frequencies (ie a running total). Each entry is the sum of all previous frequencies. You need this to find the median value.

5 The standard deviation is the measure of the spread of data. It is a measure of the average distance of values from the mean value. More specifically it is the square root of the mean squared deviations from the mean. Its formula is: Standard Deviation Use Excel formulas to calculate the last column below. It will be helpful to use an absolute reference to the cell containing the mean value in your formula, so that when you copy the formula to new rows the reference to the mean does not change. Now calculate the standard deviation in a separate cell. (You should get 1.58).

6 1.After the class has completed the following on-line Number Games question set*, upload the data file called Number_Games_Data.csv from our program space on the MASU server. Organize the data from each question into frequency tables (count up the number of people giving each response), create a bar chart, and than find the mean, mode, median and standard deviation for each question using the method you learned in this tutorial.Number Games 2.After calculating the statistics reflect on the answers a bit, did they turn out as expected? In Question 1 does the distribution look random – are people choosing number randomly as asked? In Question 2, how successful were people at choosing the same number as everyone else? If you were asked this question again, what number would you choose? In Question 3, how successful were people at not choosing the same number as everyone else? Were you successful? In Question 4, is the mean value less than in Question 1?. What is 2/3 of the value of the mean in Question 4. Did you guess right? 3.Now answer the Number Games question set again. Pay particular attention to question 4. If your goal was to choose a number equal to the mean, then the mean you calculated from question 1 might be a good guess. However, question 1 asks you to guess the number closest to 2/3 of the mean, which is less. But if everyone chooses a number smaller than the mean value in question 1, then the mean value in question 4 be smaller. Hmm … 3. Write a one page mini-paper discussing the results, using the statistics as supporting evidence. Your paper should included a comparison of means and standard deviations you calculated for each response, and offer a suggestion about why or why not you see a difference. Your paper should include an introductory paragraph introducing what you think the game theoretical idea behind the four questions might be, a main body where you use statistics to illustrate or support some point you are making, and a concluding paragraph where you state your main “findings”. You should include graphs in your paper to make direct comparisons, but do not included too many. This is a short paper. I am mainly interested in finding out how well you understand what the numbers you calculated mean. The paper is due Wednesday morning of week 2 *here is the full html address in case the above link is not accessible. You have used Excel to calculate descriptive statistics from data that is arranged in a frequency table. If the data is not in a frequency table, but is entered as raw data in a column or row, Excel has function that can calculate the mean, mode, median and standard deviation directly, without having to use the mathematical equations explicitly. In the following exercises I want you to calculate the descriptive statistics using the method in this tutorial. Lab Assignment