The mean, x, and standard deviation, s, measure center and spread, respectively,

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 different 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 Then make a stemplot of each data set and comment on the shape of each distribution including all of the data. Data set A ts 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

From the given data,

Descriptive Statistics: Data A, Data B

Total Sum of
Variable Count Mean StDev Variance Sum Squares
Data A 11 7.501 2.032 4.128 82.510 660.176
Data B 11 7.501 2.031 4.123 82.510 660.132

1) Xbar = 7.501, 7.501

2) S= 2.032, 2.031

3) Correct Answer: Optin (B)

since

Stem-and-Leaf Display: Data A, Data B

Stem-and-leaf of Data A N = 11
Leaf Unit = 0.10

1 3 1
2 4 7
2 5
3 6 1
4 7 2
(4) 8 1177
3 9 112

4) Correct Answer: Option (B)

Stem-and-leaf of Data B N = 11
Leaf Unit = 0.10

3 5 257
5 6 58
(3) 7 079
3 8 48
1 9
1 10
1 11
1 12 5

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