Home » » Find the standard derivation of the following data -5, -4, -3, -2, -1, 0, 1, 2, ...

# Find the standard derivation of the following data -5, -4, -3, -2, -1, 0, 1, 2, ...

### Question

Find the standard derivation of the following data -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5

### Options

A) 2

B) 3

C) $$\sqrt{10}$$

D) $$\sqrt{11}$$

### Explanation:

x = $$\frac{\sum x}{N}$$
= $$\frac{0}{11}$$
= 0
$$\begin{array}{c|c} x & (x - x) & (x - x)^2 \\\hline -5 & -5 & 25 \\ -4 & -4 & 16 \\-3 & -3 & 9 \\ -2 & -2 & 4 \\ -1 & -1 & 1\\ 0 & 0 & 0\\ 1 & 1 & 1\\ 2 & 2 & 4\\ 3 & 3 & 9\\ 4 & 4 & 16 \\5 & 5 & 25\\ \hline & & 110\end{array}$$
S.D = $$\sqrt{\frac{\sum(x - x)^2}{\sum f}}$$
= $$\sqrt{\frac{110}{11}}$$
= $$\sqrt{10}$$

## Dicussion (1)

• x = $$\frac{\sum x}{N}$$
= $$\frac{0}{11}$$
= 0
$$\begin{array}{c|c} x & (x - x) & (x - x)^2 \\\hline -5 & -5 & 25 \\ -4 & -4 & 16 \\-3 & -3 & 9 \\ -2 & -2 & 4 \\ -1 & -1 & 1\\ 0 & 0 & 0\\ 1 & 1 & 1\\ 2 & 2 & 4\\ 3 & 3 & 9\\ 4 & 4 & 16 \\5 & 5 & 25\\ \hline & & 110\end{array}$$
S.D = $$\sqrt{\frac{\sum(x - x)^2}{\sum f}}$$
= $$\sqrt{\frac{110}{11}}$$
= $$\sqrt{10}$$