Question

If the mean of following data is 20.6.find missing frequency x.
X-10,15,20,25,35
f-3,10,×,7,5

Answer 1

Tip: Recall the definition of mean

The mean is the arithmetic average of a set of given numbers.

The equation of mean $\overline{X}=\frac{\Sigma f_ix_i}{\Sigma f_i}$ where $x_i$ is the variable and $f_i$ is the corresponding frequency

Given:

$X: 10, 15, 20, 25, 35\\f: 3,10,x,7,5$

$\overline{X}=20.6$

Explanation:

Make a tabular column and find the corresponding values of $f_ix_i$

Refer to the image

$\Sigma f_ix_i=530+20x\\\Sigma f_i=25+x$

Mean,

$\overline{X}=\frac{\Sigma f_ix_i}{\Sigma f_i}\\\implies 20.6=\frac{530+20x}{25+x}\\\implies 20.6(25+x)=530+20x\\\implies 515+20.6x=530+20x\\\implies 20.6x-20x=530-515\\\implies 0.6x=15\\\implies x=\frac{15}{0.6} \\\implies x=25$

Hence the value of $x=25$

Answer 2

Mean, median, and mode are three kinds of "averages". There are many "averages" in statistics, but these are, I think, the three most common, and are certainly the three you are most likely to encounter in your pre-statistics courses.

Given= $x-10,15,20,25,35$

$f-3,10,x,7,5$

So, mean $=\frac{\sum x_{i}f_i}{\sum f_i}$

Mean = $\frac{(10\times3)+(15\times 10)+(20\times x)+(25\times 7)+(35\times 5)}{3+10+x+7+5}$

$=\frac{30+150+20x+175+175}{25+x}=20.6$

$=530+20x=20.6(25+x)$

$530+20x=515+20.6x$

$530-515=20.6-20x$

$15=0.6x$

$x=25$