Module 2 Assignment

1. Below is a list of the gas mileage for seven vehicles. Using the procedures we used in class, do the following:

a. Calculate the mean and standard deviation. You can do this by hand or in Excel, but please show your work (see step-by-step approach below).

b. Calculate the five number summary and make a box plot on the same set of data (this may seem a little silly since there are so few cases, but it will still work).

c. Compare the values of the mean and median (which is greater?). Is the distribution skewed (to the left or right)?

d. Which do you think (the mean or median) is a better measure of the “typical mileage” for these 7 cars?

• Vehicle A: 44 MPG
• Vehicle B: 42 MPG
• Vehicle C: 40 MPG
• Vehicle D: 36 MPG
• Vehicle E: 33 MPG
• Vehicle F: 12 MPG
• Vehicle G: 10 MPG

2. Assume that adult females’ heights are normally distributed with a mean of 66 inches and a standard deviation of 3 inches. Sketch a normal curve and draw a line in the middle for the mean, along with the approximate locations of plus and minus 1, 2, and 3 standard deviations. Based on the illustration, between what heights are approximately 95% of adult females?

STEP-BY-STEP FOR CALCULATING STANDARD DEVIATION

Manually

• 1. Calculate the average
• 2. Subtract average from the value of each individual/case in the data set.
• 3. Square each difference resulting from step 2.
• 4. Sum the squared difference from step 3. (this is the 'sum of squares').
• 5. Divide the sum of squares from step 4 by n-1 where n=the total number of observations in the dataset (this is the variance)
• 6. Take the square root of the variance from step 5 (this is that standard deviation).

Using Excel or Google sheets

Start by entering the observations/values into a column in Excel:

• 1. At the bottom of the column of observations, type the command =average(  Then highlight the whole column of observations and hit “enter”
• 2. In the cell to the right of each observation, type =  Click on the observation then the minus sign, then enter the overall average and hit “enter”  This will give you the difference for each observation.
• 3. In the cell to the right of each difference Type = into a cell, click on the difference, followed by * then click on the difference again, and “enter” This will give you the square of the difference.
• 4. At the bottom of the column of squares, type =sum(  Then highlight the whole column of squares and hit “enter.”
• 5. In a cell next to the sum of squares, type = click on the sum of squares, followed by / then enter the result of n-1 (where n=the number of observations). Hit “enter” This gives you the variance.
• 6. In a cell next to the variance, type = click on the variance, then type ^.5   Hit “enter” This will give you the square root of the variance (i.e. the standard deviation)

If you want to check your work in Excel, you can type the command =stdev(  Then highlight the whole column of values and hit “enter”