IXL - Variance and standard deviation (Precalculus practice)

In the data set below, what is the variance?

If the answer is a decimal, round it to the nearest tenth.

variance (σ²):

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Learn with an example

In the data set below, what is the variance?

If the answer is a decimal, round it to the nearest tenth.

variance (σ²):

The standard deviation (σ) is a measure of how much a data set varies.

The variance (σ²) is the square of the standard deviation.

Step
1:
Compute
the
mean,
μ
.

First add all of the numbers in the data set together. Then divide by the total number of values in the data set.

4 + 1 + 3 + 9 + 1 + 9

4.5

Step 2: Compute the variance, σ².

Take each number in the data set, subtract the mean, and square the result. Then take the sum of the squares.

(4 − 4.5)² + (1 − 4.5)² + ... + (9 − 4.5)² = 67.5

Now compute the variance by dividing the sum above by the total number of values in the data set.

σ²

67.5

11.25

Finally, round to the nearest tenth.

11.25 → 11.3

To the nearest tenth, the variance, σ², is 11.3.

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