Chapter 2: Q62E (page 103)

Using only integers between 0 and 10, construct two data sets with at least 10 observations each so that the two sets have the same mean but different variances. Construct dot plots for each of your data sets and mark the mean of each data set on its dot diagram.

Short Answer

Expert verified

Set A: 1, 0, 3, 2, 4, 2, 2, 3, 3, 0

Set B: 0, 4, 4, 4, 4, 3, 2, 0, 0, 0

Step by step solution

Creating 2 data sets only by using integers between 0 and 10

Set A: 1, 0, 3, 2, 4, 2, 2, 3, 3, 0

Mean = 2

Variance = 1.77

$Variance = \frac{\sum (x - \bar{x})^{2}}{n - 1} = \frac{{(1 - 2)}^{2} + (0 - 2)^{2} + {(3 - 2)}^{2} + {(2 - 2)}^{2} + {(4 - 2)}^{2} + {(2 - 2)}^{2} + (2 - 2)^{2} + {(3 - 2)}^{2} + {(3 - 2)}^{2} + {(0 - 2)}^{2}}{10 - 1} = \frac{1 + 4 + 1 + 0 + 4 + 0 + 0 + 1 + 1 + 4}{9} = \frac{16}{9} = 1.77$

Set B: 0, 4, 4, 4, 4, 3, 2, 0, 0, 0

Mean = 2

Variance = 3.66

$Variance = \frac{\sum (x - \bar{x})^{2}}{n - 1} = \frac{{(0 - 2)}^{2} + (4 - 2)^{2} + {(4 - 2)}^{2} + {(4 - 2)}^{2} + {(4 - 2)}^{2} + {(3 - 2)}^{2} + (2 - 2)^{2} + {(0 - 2)}^{2} + {(0 - 2)}^{2} + {(0 - 2)}^{2}}{10 - 1} = \frac{4 + 4 + 4 + 4 + 4 + 1 + 0 + 4 + 4 + 4}{9} = \frac{33}{9} = 3.66$