COMPARING TWO SETS OF DATA USING MEAN AND STANDARD DEVIATION

Example 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

Example 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 :

x


18

20

22

24

26

d = x - A

d=x-22

-4

-2

0

2

4

d2


16

4

0

4

16

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 :

x


11

14

15

17

18

d = x - A

d=x-15

-4

-1

0

2

3

d2


16

1

0

4

9

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%

So, city A is more consistent.

Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here.

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.

©All rights reserved. onlinemath4all.com

Recent Articles

  1. How to Solve Age Problems with Ratio

    Mar 28, 24 02:01 AM

    How to Solve Age Problems with Ratio

    Read More

  2. AP Calculus BC Integration of Rational Functions by Partical Fractions

    Mar 26, 24 11:25 PM

    AP Calculus BC Integration of Rational Functions by Partical Fractions (Part - 1)

    Read More

  3. SAT Math Practice

    Mar 26, 24 08:53 PM

    satmathquestions1.png
    SAT Math Practice - Different Topics - Concept - Formulas - Example problems with step by step explanation

    Read More