The mean, X, and standard deviation, s, measure center and spread, respectively,
ID: 3222908 • Letter: T
Question
The mean, X, and standard deviation, s, measure center and spread, respectively, but are not a complete description of a distribution. Data sets with deferent shapes can have both the same mean and the same standard deviation. To demonstrate this fact, find x and s for each of these two small data sets. Then report what this common mean and this common standard deviation are. Data A 9.14 8.14 8.74 8.77 9.26 8.10 6.13 3.10 9.13 7.26 4.74 Data B 6.58 5.76 7.71 8.84 8.47 7.04 5.25 5.56 7.91 6.89 12.50 x = 7.58 s = Then make a stem plot of each data set and comment on the shape of each distribution including all of the data. Data set A is symmetric. Data set A is skewed left. Data set A is skewed right. Data A Data set B is skewed left. Data set B is skewed right. Data set B is symmetric.Explanation / Answer
Xbar = 7.501
s = 1.937
Stem and Leaf
Hence Data A is skewed to left and Data B is skewed to right
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 7.501 7.501 std. dev. 1.937 1.936