Question

find the standard deviation of the given data. now, find the variance, or the average of the squares of the differences. data: 5, 6, 8, 13; data - \\(\bar{x}\\): -3, -2, 0, 5; \\((\text{data} - \bar{x})^2\\): 9, 4, 0, 25; variance (\\(\sigma^2\\)) = \\(\frac{9 + 4 + 0 + 25}{4}\\) = ?

Explanation:

Step1: Sum the numerator terms

First, we add the numbers in the numerator: \(9 + 4 + 0 + 25\).
\(9+4 = 13\), \(13 + 0 = 13\), \(13 + 25 = 38\).

Step2: Divide by the number of data points

Now, we divide this sum by the number of data points, which is 4. So we calculate \(\frac{38}{4}\).
\(\frac{38}{4}=9.5\)

Answer:

\(9.5\)