In a continuous frequency distribution, the median of the data is 21.If each observation is increased by 5 find the new median

Answer :
Given  :
In a continuous frequency distribution, the median of the data is 21.
And
If each observation is increased by 5 .

Then the new median is also increased by 5 , so new median  =  21  +  5  =  26  ( Ans )

We can understand it As :


Suppose there are 20 children and the number of toys with each child is given below :

3, 5, 6, 6, 8, 8, 9, 9, 10, 11, 11, 12, 12, 12, 14, 15, 15, 18, 18, 20

First we form a continuous frequency table , As  :
 
Number of toys 0 - 5 5 - 10 10 - 15 15 - 20 20-25
Frequency 1 7 7 4 1

Here frequency is number of children that have toys in between ( 0 -5  ,  5 - 10 , 10- 15 , 15 - 20 , 20-25)


 
CLASS INTERVALS Frequency Cumulative Frequency
0-5 1 1
5-10 7 8
10-15 7 15
15-20 4 19
20-25 1 20


Now, median class is 10-15
lower limit of median class = 10
Frequency of median class, f = 7
Cumulative frequency of the class preceeding median class, cf = 8
Class size, h = 5

Median = l + n/2 - cff×h=10 + 10-87×5=10 + 107=807

When each of the given observation is increased by 5, then we get

8,10,11,11,13,13,14,14,15,16,16,17,17,17,19,20,20,23,23,25
 
CLASS INTERVALS FREQUENCY CUMULATIVE FREQUENCY
0-5 0 0
5-10 1 1
10-15 7 8
15-20 7 15
20-25 4 19
25-30 1 20

Now, median class is 15-20
lower limit of median class = 15
Frequency of median class, f = 7
Cumulative frequency of the class preceeding median class, cf = 8
Class size, h = 5

Median = l + n/2 - cff×h=15 + 10-87×5=1157increase in median = 1157 - 807 = 357 = 5
 

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