Find the mean, median and mode of the following data:

Classes:	0-20	20-40	40-60	60-80	80-100	100-120	120-140
Frequency:	6	8	10	12	6	5	3

To do:

We have to find the mean, median and mode of the following data.

Solution:

The frequency of the given data is as given below.

Let the assumed mean be $A=70$.

We know that,

Mean $=A+\frac{\sum{f_id_i}}{\sum{f_i}}$

Therefore,

Mean $=70+(\frac{-380}{50})$

$=70-7.6$

$=62.4$

The mean of the given data is 62.4.

We observe that the class interval of 60-80 has the maximum frequency(12).

Therefore, it is the modal class.

Here,

$l=60, h=20, f=12, f_1=10, f_2=6$

We know that,

Mode $=l+\frac{f-f_1}{2 f-f_1-f_2} \times h$

$=60+\frac{12-10}{2 \times 12-10-6} \times 20$

$=60+\frac{2}{24-16} \times 20$

$=60+\frac{40}{8}$

$=60+5$

$=65$

The mode of the given data is 65.

Here,

$N=50$

This implies, $\frac{N}{2}=\frac{50}{2}=25$

Median class $=60-80$

We know that,

Median $=l+\frac{\frac{N}{2}-F}{f} \times h$

$=60+\frac{25-24}{12} \times 20$

$=60+\frac{20}{12}$

$=60+1.66=61.66$

The median of the given data is 61.66.

The mean, mode and median of the above data are 62.4, 65 and 61.66 respectively.  

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Updated on: 10-Oct-2022

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