All the students of a class performed poorly in mathematics. Thr teacher decided to give grace marks of 10 to each of the students. which of the following statistical measures will not change even after the grace were given ?

a. mean

b. median

c. mode

d. variance

Ans is 4. variance

Please explain that why the median is changed .

Let the numbers be 30 , 35 , 30 , 40 ,45 , 30 , 40

Means of these is average = ( 30 + 35 + 30 + 40+45 + 30 +40 )/ 7 = 35.71
Median is the middle data of arranged data.
So arrange the data in ascending order = 30, 30,30 , 35 , 40, 40 , 45
So here the middle data is 35, so median is 35.

And mode is the maximum frequency of data, in the above data, 30 occured most frequently, so 30 is the mode.

And variance = summation of  (xi - mean)2 /number of data

(35-35.71)2+(30-35.71)2+(30-35.71)2+(30-35.71)2 + (40-35.71)2+ (40-35.71)2+ (45-35.71)27=
 = 31.63

If 10 is added to each data, we can see that mean , median and mode are changed, follow the same process to find them.

And the variance =  (45-45.71)2+(40-45.71)2+(40-45.71)2+(40-45.71)2 + (50-45.71)2+ (50-45.71)2+ (55-45.71)27
= 31.63
Hence the median get changed and variance remains same.

  • 5

Of course median will change.

E.g = if the median was say for 21 which is the middle value after adding 10 to it will become 31

  • -4
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