If the mean of the frequency distribution Class : 0-10 10-20 20-30 30-40 40-50 Frequency :…

Question

If the mean of the frequency distribution

Class :
 0-10
 10-20
 20-30
 30-40
 40-50

Frequency :
 2
 3
 $x$
 5
 4

is 28, then its variance is \_\_\_\_\_\_\_\_\_\_.

Answer: 151

Accepted Answer

Given mean is 28

$\begin{gathered} \frac{2	imes 5+3	imes 15+x	imes 25+5	imes 35+4	imes 45}{14+x}=28 \ \Rightarrow \frac{10+45+25x+175+180}{14+x}=28 \ \Rightarrow 310+25x=392+28x \ \Rightarrow 3x=18\Rightarrow x=6 \end{gathered}$

$\begin{gathered} 	herefore =(\frac{\sum {x}_{2}^{i}{f}_{i}}{\sum {f}_{i}})-({)}^{2} \ =(\frac{2	imes {5}^{2}+3	imes {15}^{2}+6	imes {25}^{2}+5	imes {35}^{2}+4	imes {45}^{2}}{20})-(28{)}^{2} \ =(\frac{50+675+3750+6125+8100}{20})-(28{)}^{2} \ =(\frac{18700}{20})-(28{)}^{2} \ =935-784=151 \end{gathered}$

Solutions · 1