Question

Fund the deviation about mean the following data
Xi 5,10,15,20,25
fi 7,4,6,3,5​

Answer 1

Answer:

firstly we have to find out the mean by using formula ,

\overline{x}=\frac{\sum{f_ix_i}}{\sum{f_i}}

x

=

∑f

i

∑f

i

x

i

and then calculate mean deviation by using the formula ,

MD=\frac{\sum{(f_i|x_i-\overline{x}|)}}{\sum{f_i}}MD=

∑f

i

∑(f

i

∣x

i

−

x

∣)

see attachment ,

here,

$$\begin{lgathered}\sum{f_i}=25\\\\\sum{f_ix_i}=350\\\\\\so,Mean(\overline{x})=\frac{\sum{f_ix_i}}{\sum{f_i}}=\frac{350}{25}\\\\=14\end{lgathered}$$

now,

from data ,

$$\begin{lgathered}\sum{f_i|x_i-\overline{x}|}=158\\\\now,mean\: deviation\:about\:mean=\frac{\sum{f_i|x_i-\overline{x}|}}{\sum{f_i}}\\\\=\frac{158}{25}\\\\=6.32\end{lgathered}$$