To find: The number of standard deviations from the mean that include all the data values given.
The data falls within 2 standard deviations of the mean.
Given information:
The given data set is 12,17,15,13,9,10,12,10,15,17.
Calculation:
The mean of the data is given by:
To determine the variance, the following table is used:
12 | 13 | -1 | 1 |
17 | 13 | 4 | 16 |
15 | 13 | 2 | 4 |
13 | 13 | 0 | 0 |
9 | 13 | -4 | 16 |
10 | 13 | -3 | 9 |
12 | 13 | -1 | 1 |
10 | 13 | -3 | 9 |
15 | 13 | 2 | 4 |
17 | 13 | 4 | 16 |
Sum | 76 |
Hence,
The standard deviation is given by:
The minimum and maximum values of the data are 9 and 17, respectively.
1 standard deviation below the mean:
2 standard deviations below the mean:
Hence the minimum value falls within two standard deviations of the mean.
1 standard deviation above the mean:
2 standard deviations above the mean:
Hence the maximum value falls within two standard deviations of the mean.
Conclusion:
The data falls within 2 standard deviations of the mean.
Chapter 11 Solutions
High School Math 2015 Common Core Algebra 2 Student Edition Grades 10/11
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