**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.

**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 :**

x 18 20 22 24 26 |
d = x - A d=x-22 -4 -2 0 2 4 |
d 16 4 0 4 16 |

Σd^{2}/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%

x 11 14 15 17 18 |
d = x - A d=x-15 -4 -1 0 2 3 |
d 16 1 0 4 9 |

Σd^{2}/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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