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Math  /  Data & Statistics

QuestionIn the data set below, what is the standard deviation? 61178\begin{array}{lllll}6 & 1 & 1 & 7 & 8\end{array}
If the answer is a decimal, round it to the nearest tenth. standard deviation (σ)(\sigma) : □\square Submit

Studdy Solution

STEP 1

1. The data set consists of the numbers: 6,1,1,7,8 6, 1, 1, 7, 8 .
2. We are calculating the population standard deviation, not the sample standard deviation.
3. The answer should be rounded to the nearest tenth.

STEP 2

1. Calculate the mean of the data set.
2. Calculate the squared deviations from the mean.
3. Calculate the variance.
4. Calculate the standard deviation by taking the square root of the variance.

STEP 3

Calculate the mean of the data set.
Mean=6+1+1+7+85=235=4.6\text{Mean} = \frac{6 + 1 + 1 + 7 + 8}{5} = \frac{23}{5} = 4.6

STEP 4

Calculate the squared deviations from the mean.
(6−4.6)2=1.96(6 - 4.6)^2 = 1.96 (1−4.6)2=12.96(1 - 4.6)^2 = 12.96 (1−4.6)2=12.96(1 - 4.6)^2 = 12.96 (7−4.6)2=5.76(7 - 4.6)^2 = 5.76 (8−4.6)2=11.56(8 - 4.6)^2 = 11.56

STEP 5

Calculate the variance by taking the average of the squared deviations.
Variance=1.96+12.96+12.96+5.76+11.565=45.25=9.04\text{Variance} = \frac{1.96 + 12.96 + 12.96 + 5.76 + 11.56}{5} = \frac{45.2}{5} = 9.04

STEP 6

Calculate the standard deviation by taking the square root of the variance.
σ=9.04≈3.0\sigma = \sqrt{9.04} \approx 3.0
The standard deviation is:
σ=3.0\sigma = \boxed{3.0}

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