Statistics Describing, Exploring and Comparing Data Chapter 3 Example Problems

Measures of Variation Objective: Find the range, variance and standard deviation of sample data Question: Statistics students participated in an experiment to test their ability to determine when I minute (or 60 seconds) has passed. The results are given below in seconds. Find the range, variance, and standard deviation for the given sample data. Identify one reason why the standard deviation from this sample might not be a good estimate of the standard deviation for the population of adults. 55 51 64 70 49

Measures of Variation Range: The difference between the high and low values Range = High – Low = 70 – 49 = 21 seconds 55 51 64 70 49

Measures of Variation Sample variance: measure of variation of values (from a sample) from the mean You want to learn with a small sample how to compute the sample standard deviation for your understanding but then you want to move to technology as it will be faster. So let’s do this one both ways. The formula for the sample variance is , where x is each sample value, that is 55, 51, 64, 70 and 49 and is the mean of the sample, that is (55+51+64+70+49)/5 = 57.8 and n is the number of samples which is 5. 55 51 64 70 49

Measures of Variation So the sample variance is taking each x value, subtracting the mean, square this and summing these up, that is As you can see already this is a lot of calculations but this is good to know that this is how the formula works. You can go through and simplify the parentheses, then square to get 55 51 64 70 49

Measures of Variation seconds Remember to then get the sample standard deviation to simply take the square root of 79.7 seconds

MEASURES OF VARIATION Technology Way In your TI-83/84 you first have to put the values in a list. STAT / EDIT / 1:Edit Enter Enter each of the values 55, 51, 64, 70, 49 (pressing enter to move down after each one) Then press STAT / CALC / 1-Var Stats / Enter and put the L1 list you created by 2nd 1 and press Enter. You will see the mean of 57.8 that we found and the 8.9 standard deviation. 55 51 64 70 49

55 51 64 70 49