Question

Calculate the mean of the following distribution:

Cl	0-10	10-20	20-30	30-40	40-50
b	12	16	6	7	9

Answer 1

Hint: As we know, the mean is the average of the data. In this question, we need to calculate the mean of grouped data. To calculate mean of grouped data given, we have formula $\overline x = \dfrac{{\sum {{f_i}{x_i}} }}{{\sum {{f_i}} }}$ . Now, we have to put the values in the formula to get the mean of the given data.

Complete step-by-step answer:
We know, mean of the given data is calculated by:
$\overline x = \dfrac{{\sum {{f_i}{x_i}} }}{{\sum {{f_i}} }}$
Where,
 \[{x_i}\] = mid value of the class interval
${f_i}$ = frequency of the class
Now, we need to find all the above values in a tabular form.

Class interval	Frequency (${f_i}$ )	Mid value(${x_i}$ )	${f_i}{x_i}$
0-10	12	5	60
10-20	16	15	240
20-30	6	25	150
30-40	7	35	245
40-50	9	45	405
Total	50		1100

Now, putting all the values in the above formula

$
\Rightarrow \overline x = \dfrac{{\sum {{f_i}{x_i}} }}{{\sum {{f_i}} }} \\
\Rightarrow \overline x = \dfrac{{1100}}{{50}} \\
\Rightarrow \overline x = 22 \\
 $
Therefore, the mean of the given data is 22.

Note: Mean can be calculated by three different methods that are the direct method which is used above, assumed mean method and step-deviation method. Any of the methods can be used to calculate mean.