# COMPARING WHOSE PERFORMANCE IS BETTER WITH MEAN AND STANDARD DEVIATION

Comparing Whose Performance is Better with Mean and Standard Deviation :

Here we are going to see, how to compare whose performance is better with mean and standard deviation.

## Comparing Whose Performance is Better with Mean and Standard Deviation - Examples

Question 1 :

The mean and standard deviation of marks obtained by 40 students of a class in three subjects Mathematics, Science and Social Science are given below Which of the three subjects shows highest variation and which shows lowest variation in marks?

Solution :

Mathematics :

Coefficient of variation (C.V) =  (σ/x̄) ⋅ 100%

x̄  =  56, σ  =  12

C.V  =  (12/56⋅ 100%

C.V  =  0.2142 ⋅ 100%

C.V  =  21.42%

Science :

Coefficient of variation (C.V) =  (σ/x̄) ⋅ 100%

x̄  =  65, σ  =  14

C.V  =  (14/65⋅ 100%

C.V  =  0.2153 ⋅ 100%

C.V  =  21.53%

Social Science :

Coefficient of variation (C.V) =  (σ/x̄) ⋅ 100%

x̄  =  60, σ  =  10

C.V  =  (10/60⋅ 100%

C.V  =  0.1666 ⋅ 100%

C.V  =  16.66%

The highest variation is in the subject Science and lowest variation is in the subject Social science

Question 2 :

The temperature of two cities A and B in a winter season are given below. Find which city is more consistent in temperature changes?

Solution : ## Temperature of city A :

 x1820222426 d = x - Ad=x-22-4-2024 d21640416

Σd2/n  =  40/5  =  8

(Σd/n)2  =  (0)2  =  0

σ  =  √(8 - 0)

=  √8

σ  =  2.82

Mean (x̄)  =  (18 + 20 + 22 + 24 + 26)/ 5

= 110/5

x̄  = 22

Coefficient of variation (C.V) =  (σ/x̄) ⋅ 100%

x̄  =  22, σ  =  2.82

C.V  =  (2.82/22⋅ 100%

C.V  =  0.1281⋅ 100%

C.V  =  12.81%

## Temperature of city B :

 x1114151718 d = x - Ad=x-15-4-1023 d2161049

Σd2/n  =  30/5  =  6

(Σd/n)2  =  0

σ  =  √(6 - 0)

=  √6

σ  =  2.44

x̄  =  Σx/n

=  (11+14+15+17+18)/5

x̄  =  75/5

x̄  =  15

Coefficient of variation (C.V) =  (σ/x̄) ⋅ 100%

C.V  =  (2.44/15⋅ 100%

C.V  =  (244/1500) ⋅ 100%

C.V  =  0.1626 ⋅ 100%

C.V  =  16.26%

Hence city A is more consistent. After having gone through the stuff given above, we hope that the students would have understood, "Comparing Whose Performance is Better with Mean and Standard Deviation".

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