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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.