Question 5.71

41. The mean and standard deviation are not generally a complete description. Datasets with different shapes can have the same mean and standard deviation.

  1. To demonstrate this fact, use your calculator (or software) to find and for the two small datasets below.
  2. Make a stemplot of each dataset and comment on the shape of each distribution. (Either round or truncate data values to one decimal place.)
Dataset A: 9.14 8.14 8.74 8.77
9.26 8.10 6.13 3.10
9.13 7.26 4.74
Dataset B: 7.46 6.77 12.74 7.11
7.81 8.84 6.08 5.39
8.15 6.42 5.73

41.

(a) Using the TI-83, we have the following for datasets A and B, respectively:

image

Thus, for each data set we have and .

(b) From the stemplots below, we observe that dataset A has two low potential outliers and dataset B has one high potential outlier. (For these stemplots, the data have been rounded.)

Dataset A:

image

Dataset B:

image