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Grade -10 (SEE) Math Median, Statistics

Find the median from the date given below – Statistics

Find the median from the data given below:

Class Interval 40-50 50-60 60-70 70-80 80-90
Frequency 7 8 6 5 4
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Tribhuvan University > Institute of Science and Technology > B.Sc. (CSIT)

Solution:

Here,

Preparing a cumulative frequency table to calculate median from the given data, we get

Class (X) Frequency (f) Cumulative frequency (cf)
40-50 7 7
50-60 8 7+8=15
60-70 6 15+8=21
70-80 5 21+5=26
80-90 4 26+4=30
  N=30  

Using formula,

Median (Md) = The value of (N/2)th item
= (30/2)th item
= 15th item

here,

The corresponding class of cf 15 is 50-60

∴ Median class = 50-60

Again, by formula

Actual median (Md) = \(L+\frac{\left(\frac{N}{2}-cf\right)}{f}\cdot i\)

Where,

L = 50,
N/2 = 15
cf = 7
f = 8
i = 10

So, Actual median (Md) 

= \(50+\frac{\left(15-7\right)}{8}\cdot10\)
= 60

∴ Median of the given data is 60.

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