Question

find the standard deviation of the given data.
$overline{x} = 8$
next, find the square of the differences.
data \t 5 \t 6 \t 8 \t 13
data $- overline{x}$ \t $-3$ \t $-2$ \t 0 \t 5
$(\text{data} - overline{x})^2$ \t 9 \t 4 \t 0 \t ?
$(5)^2 = ?$

Explanation:

Step1: Calculate \((\text{Data}-\overline{x})^2\) for 13

We know that \(\text{Data}-\overline{x} = 5\) for the data point 13. To find \((\text{Data}-\overline{x})^2\), we square 5.
\(5^2 = 25\)

Step2: Calculate \(5^2\)

Squaring the number 5, we use the formula \(a^2=a\times a\). So \(5^2 = 5\times5=25\)

Answer:

For \((\text{Data}-\overline{x})^2\) when data is 13: 25
For \(5^2\): 25