Chapter 12: Q13. (page 801)

GRIDDED RESPONSE Find the standard deviation of the set of data below to the nearest tenth.

Short Answer

Expert verified

The standard variation of the given data set is $3.14$ .

Step by step solution

Step 1. Find the mean.

To find the mean, add the numbers and then divide by the number of values in the data set.

$\begin{array}{l} \bar{x} = \frac{14 + 11 + 9 + 6 + 10 + 16 + 15 + 13 + 9 + 12 + 19 + 10}{12} \\ = \frac{144}{12} \\ = 12 \end{array}$

Step 2. Find the variance.

To find the variance, square the difference between each number and the mean. Then add the squares, and divide by the number of values.

$\begin{array}{l} σ^{2} = \frac{{(14 - 12)}^{2} + {(11 - 12)}^{2} + {(9 - 12)}^{2} + {(6 - 12)}^{2} + {(10 - 12)}^{2} + {(16 - 12)}^{2} + {(15 - 12)}^{2} + {(13 - 12)}^{2} + {(9 - 12)}^{2} + {(12 - 12)}^{2} + {(19 - 12)}^{2} + {(10 - 12)}^{2}}{12} \\ = \frac{{(2)}^{2} + {(- 1)}^{2} + {(- 3)}^{2} + {(- 6)}^{2} + {(- 2)}^{2} + {(4)}^{2} + {(3)}^{2} + {(1)}^{2} + {(- 3)}^{2} + {(0)}^{2} + {(7)}^{2} + {(- 2)}^{2}}{12} \\ = \frac{4 + 1 + 9 + 12 + 4 + 16 + 9 + 1 + 9 + 49 + 4}{12} \\ = \frac{118}{12} \\ = 9.83 \end{array}$

Step 3. Find the standard deviation.

To find the standard deviation, take square root of the variance.

$\begin{array}{l} σ^{2} = 9.83 \\ σ = \sqrt{9.83} \\ \approx 3.14 \end{array}$

Therefore, the standard variation of the given data set is $3.14$ .

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GRIDDED RESPONSE Find the standard deviation of the set of data below to the nearest tenth.

Short Answer

Step by step solution

Step 1. Find the mean.

Step 2. Find the variance.

Step 3. Find the standard deviation.

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