Question

IF 5 are added to each Observation of the data, what will be the difference in the Median ?
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Answer 1

Answer:

The Median is also increased by 5.

Step-by-step explanation:

Given :-

If 5 is added to each Observation of the data

To find :-

What will be the difference in the Median ?

Solution :-

We know that The middle term of the given data when it is arranged in either ascending order or descending order is called its Median.

Let x1,x2,x3,...,xn observations having xr as it's median

On adding 5 to each term then

x1+5,x2+5,...,xr+5,...,xn+5

The Median is xr+5

The median is Increased by 5

Answer :-

If each term is increased by 5 then the median is also increased by 5.

Check:-

Consider a data :

1,3,5,8,9

The number of observations is odd

The median is (n+1)/2th observation.

=> (5+1)/2 = 6/2 = 3rd observation

The median = 5

If 5 is added to each observation then

1+5,3+5,8+5,9+5

=> 6,8,10,13,14

The median = 10 = 5+5

The Median is Increased by 5

Consider a data :

7,9,13,15,21,25

The number of observations is even

The median is the average of (n/2)th and (n/2)+1th observations

=> n/2 6/2 = 3rd observation = 13

n/2+1= 3+1 = 4th observation = 15

Median = (13+15)/2 = 28/2 = 14

If 5 is added to each observation then

7+5,9+5,13+5,15+5,21+5,25+5

=> 12,14,18,20,26,30

The median = (18+20)/2

= 38/2

= 19

= 14+5

The Median is Increased by 5

Verified the given relations in the given problem.

Points to know:-

Median:-

• A median is the middle term of the given data when it is arranged in either ascending order or descending order .
• It is denoted by M
• If the number of observations is n , an odd then the median is (n+1)/2 th observation.
• If the number of observations is n , an even then the median is the average of (n/2)th and (n/2)+1th observations.
• If the Median of a data is M and each term is increased by K then the new median is M+K . i.e. the Median is also increased by K. Where K is a real number.