The variance ^2 of the data x_i 0 1 5 6 10 12 17 f_i 3 2 3 2 6 3 3 is _________.

Question

The variance ${\sigma }^{2}$ of the data

${x}_{i}$
 0
 1
 5
 6
 10
 12
 17

${f}_{i}$
 3
 2
 3
 2
 6
 3
 3

is \_\_\_\_\_\_\_\_\_.

Answer: 29

Accepted Answer

${x}_{i}$
 ${f}_{i}$
 ${f}_{i}{x}_{i}$
 ${f}_{i}{x}_{2}^{i}$

0
 3
 0
 0

1
 2
 2
 2

5
 3
 15
 75

6
 2
 12
 72

10
 6
 60
 600

12
 3
 36
 432

17
 3
 51
 867

$\Sigma {f}_{i}=22$

$\Sigma {f}_{i}{x}_{2}^{i}=2048$

$\begin{gathered} 	herefore \, \Sigma {f}_{i}{X}_{i}=176 \ \vec{x}=\frac{\sum {f}_{i}{x}_{i}}{\sum {f}_{i}}=\frac{176}{22}=8 \ {\sigma }^{2}=\frac{1}{N}\sum {f}_{i}{x}_{i}{}^{2}-(\vec{x}{)}^{2} \ =\frac{1}{22}	imes 2048-(8{)}^{2} \ =93.090964 \ =29.0909 \end{gathered}$

Solutions · 1