To find: The standard deviation for each year is to be determined and are to be used to describe how farm income varied from 2001 to 2002.
The standard deviations for the years 2001 and 2002 are 2678.9 and 2758.99 respectively.
Since the second data set has a larger standard deviation, the data set is much more spread out than the data in the first data set.
Given information:
The given data sets are:
The mean income for the years 2001 and 2002 are 6706.86 and 6738.14 (millions of dollars) respectively.
Calculation:
To determine the variance, the following table is used:
10653 | 6706.86 | 3946.14 | 15572021 |
7979 | 6706.86 | 1272.14 | 1618340.2 |
7537 | 6706.86 | 830.14 | 689132.42 |
4723 | 6706.86 | -1983.86 | 3935700.5 |
9221 | 6706.86 | 2514.14 | 6320899.9 |
2938 | 6706.86 | -3768.86 | 14204306 |
3897 | 6706.86 | -2809.86 | 7895313.2 |
50235713 |
Hence,
The standard deviation is given by:
The standard deviation for the first data set is 2678.9.
To determine the variance, the following table is used:
10834 | 6738.14 | 4095.86 | 16776069 |
7862 | 6738.14 | 1123.86 | 1263061.3 |
7478 | 6738.14 | 739.86 | 547392.82 |
4402 | 6738.14 | -2336.14 | 5457550.1 |
9589 | 6738.14 | 2850.86 | 8127402.7 |
3223 | 6738.14 | -3515.14 | 12356209 |
3779 | 6738.14 | -2959.14 | 8756509.5 |
53284195 |
Hence,
The standard deviation is given by:
The standard deviation for the first data set is 2758.99.
Conclusion:
The standard deviations for the years 2001 and 2002 are 2678.9 and 2758.99 respectively.
Since the second data set has a larger standard deviation, the data set is much more spread out than the data in the first data set.
Chapter 11 Solutions
High School Math 2015 Common Core Algebra 2 Student Edition Grades 10/11
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