Question

calculate standard deviation of a population

60, 58, 53, 49, 60

the mean of the data set is 56

\\\sigma^2 = \frac{(x_1 - \mu)^2 + (x_2 - \mu)^2 + \dots + (x_n - \mu)^2}{n}\\

what does the numerator evaluate to?
what does the denominator evaluate to?
the variance equals
standard deviation
\\(\sigma \approx\\)

Explanation:

Identify the given values and formula

Using the Population Variance Calculation knowledge point

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Calculate the standard deviation

The population standard deviation \(\sigma\) is the square root of the population variance \(\sigma^2\):

$$ \sigma = \sqrt{\sigma^2} = \sqrt{18.8} \approx 4.34 $$

Answer:

Calculate Standard Deviation of a Population

Data set: \(60, 58, 53, 49, 60\)
The mean of the data set is 56.

What does the numerator evaluate to? <blank>94</blank>
What does the denominator evaluate to? <blank>5</blank>
The variance equals <blank>18.8</blank>
Standard deviation \(\sigma \approx\) <blank>4.34</blank>