Chapter 12: Q12. (page 797)

Find the mean, variance, and standard deviation to the nearest tenth for each set of data.
$10, 10, 12, 14$

Short Answer

Expert verified

The mean, variance and standard variation of the given data set is $11.5, 2.75$ and $1.658$ respectively.

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.

$\begin{array}{l} \bar{x} = \frac{10 + 10 + 12 + 14}{4} \\ = \frac{46}{4} \\ = 11.5 \end{array}$

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.

$\begin{array}{l} σ^{2} = \frac{{(10 - 11.5)}^{2} + {(10 - 11.5)}^{2} + {(12 - 11.5)}^{2} + {(14 - 11.5)}^{2}}{4} \\ = \frac{{(- 1.5)}^{2} + {(- 1.5)}^{2} + {(0.5)}^{2} + {(2.5)}^{2}}{4} \\ = \frac{2.25 + 2.25 + 0.25 + 6.25}{4} \\ = \frac{11}{4} \\ = 2.75 \end{array}$

Step 3. Find the standard deviation.

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

$\begin{matrix} σ^{2} = 2.75 \\ σ = \sqrt{2.75} \\ \approx 1.658 \end{matrix}$

Therefore, the mean, variance and standard variation of the given data set is $11.5, 2.75$ and $1.685$ respectively.

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Find the mean, variance, and standard deviation to the nearest tenth for each set of data.
$10, 10, 12, 14$

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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Find the mean, variance, and standard deviation to the nearest tenth for each set of data.10,10,12,14

Short Answer

Step by step solution

Step 1. Find the mean.

Step 2. Find the variance.

Step 3. Find the standard deviation.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Mechanics Maths

Statistics

Discrete Mathematics

Probability and Statistics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Find the mean, variance, and standard deviation to the nearest tenth for each set of data.
$10, 10, 12, 14$