Question

Write the median class of the following distribution:
Class-interval:
0−10
10−20
20−30
30−40
40−50
50−60
60−70
Frequency:
4
4
8
10
12
8
4

Answer 1

SOLUTION :  

CUMULATIVE FREQUENCY DISTRIBUTION TABLE is in the attachment

Here, n = 50

n/2 = 25

Since, the Cumulative frequency just greater than 25  is 26 and the corresponding class is 30 - 40 . Therefore 30 - 40 is the median class.

★★ Median class is the class whose Cumulative  frequency is greater than (and nearest to)  n/2.

★★ CUMULATIVE FREQUENCY: Cumulative frequency is defined as a consecutive sum of frequencies. The Cumulative frequency of first observation is the same as its frequency since there is no frequency before it.

HOPE THIS ANSWER WILL HELP YOU……

Answer 2

To find the median class, The Cumulative frequency of the given data is needed.

After that, We divide the total of frequency (not cumulative) with 2 and then what comes out after dividing it with 2, we compare it with the Cumulative frequency, Now how this comparison happens --

For this data,

n/2 = 50/2 = 25

So, we see a slightly bigger value from 25 in cumulative frequency which is 26 (according to this data)

So the class corresponding to this cumulative frequency will be the Median class.

So, Class interval corresponding to 26 is 30 - 40,

So 30 - 40 is the median class

While finding the median of grouped data, Median class is required.

Here, lower value of median class, n/2, Frequency of median class, cumulative frequency, difference between intervals of median class is required.

Note - While finding the median we don't take the Cumulative frequency we took to find the median class, we take the Cumulative frequency before that cumulative frequency we used to find the median class.