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

Classes:	0-50	50-100	100-150	150-200	200-250	250-300	300-350
Frequency:	2	3	5	6	5	3	1

To do:

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

Solution:

The frequency of the given data is as given below.

Let the assumed mean be $A=175$.

Here, $\sum{f_id_i}=-150$ and $\sum{f_i}=25$

We know that,

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

Therefore,

Mean $=175+(\frac{-150}{25})$

$=175-(6)$

$=169$

The mean of the given data is 169.

We observe that the class interval of 150-200 has the maximum frequency(6).

Therefore, it is the modal class.

Here,

$l=150, h=50, f=6, f_1=5, f_2=5$

We know that,

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

$=150+\frac{6-5}{2 \times 6-5-5} \times 50$

$=150+\frac{1}{12-10} \times 50$

$=150+\frac{50}{2}$

$=150+25$

$=175$

The mode of the given data is 175.

Here,

$N=25$

This implies, $\frac{N}{2}=\frac{25}{2}=12.5$

Median class $=150-200$

We know that,

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

$=150+\frac{12.5-10}{6} \times 50$

$=150+\frac{2.5 \times 50}{6}$

$=150+\frac{125}{6}$

$=150+20.83$

$=170.83$

The median of the given data is 170.83.

The mean, mode and median of the above data are 169, 175 and 170.83 respectively. 

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Updated on: 10-Oct-2022

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