The mean x bar and standard deviation s measure center and spread but are not a

Question

The mean x bar and standard deviation s measure center and spread but are not a complete description of a distribution. Data sets with different shapes can have the same mean and standard deviation. To demonstrate this fact, use your calculator to find x bar and s for these two small data sets. Then make a stemplot of each and comment on the shape of each distribution. The shape of a distribution is a rough guide to whether the and standard deviation are a helpful summary of center and spread. For which of the following distributions would x bar and s be useful In each case, give a reason for your decision. Percents of high school graduates in the states taking the SAT, Figure 1.8

Explanation / Answer

Following table shows the mean and standard deviation of data set A and B :

The above table shows that both data set have approximately same mean and standard deviation.

Following is the stemplot of data set A:

Following is the stem and leaf plot of data set B :

Stem-and-leaf plot shows that distribution of data set is left skwed while distribution of data set B is right skewed.  

Data A Data B 9.14 6.58 8.14 5.76 8.74 7.71 8.77 8.84 9.26 8.47 8.1 7.04 6.13 5.25 3.1 5.56 9.13 7.91 7.26 6.89 4.74 12.5 Mean 7.500909091 7.500909091 SD 2.031656736 2.030578511

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