Look at the frequency distribution table given below: Class inter… - Vidyadip

MCQ

Look at the frequency distribution table given below:

Class interval	$35-45$	$45-55$	$55-65$	$65-75$
Frequency	$8$	$12$	$20$	$10$

The median of the above distribution is:

A
$56.5$
✓
$57.5$
C
$58.5$
D
$59$

✓

Answer

Correct option: B.

$57.5$

Class intervalClass interval	FrequencyFrequency	Cumulative frequencyCumulative frequency
$35-45$	$8$	$8$
$45-55$	$12$	$20$
$55-65$	$20$	$40$
$65-75$	$10$	$50$

Here, $\text{N}=50$
$\Rightarrow\frac{\text{N}}{2}=25$
The cumulaove frequency just greater than $25$ is $40.$
Hence, median class is $55-65.$
Now, median $=\text{l}+\begin{Bmatrix}\text{h}\times\frac{\Big(\frac{\text{N}}{2}-\text{cf}\Big)}{\text{f}}\end{Bmatrix}$
$=55+\Big\{10\times\frac{(25-20)}{20}\Big\}$
$=55+2.5$
$=57.5$

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