Question

The following table gives weights of
the students of two classes. Calculate
the coefficient of variation of the two
distributions. Which series is more variable?
Weight (in kg) Class A Class B
30-40 I 22 I 13
I 40-50
16 I 10
50-60 I 12 I 17
​

Answer 1

Answer:

CV of class A = 30.2%

CV of class B = 26.35%

Step-by-step explanation:

We are given the following table of weights of  the students of two classes ;

          Weight (in kg)        Class A          Class B

              30 - 40                  22                    13

               40 - 50                  16                     10

               50 - 60                  12                     17

Coefficient of variation formula = $\frac{Standard deviation}{Mean} * 100$

• Coefficient of Variation of class A ;

          Mean =  $\frac{22+16+12}{3}$ = 16.67

          Standard deviation = $\sqrt{\frac{(22-16.67)^{2} +(16-16.67)^{2} + (12-16.67)^{2} }{3-1} }$ = 5.033

          C.V. =   $\frac{Standard deviation}{Mean} * 100$ = $\frac{5.033}{16.67} * 100$ = 30.2%

• Coefficient of Variation of class B ;

           Mean = $\frac{13+10+17}{3}$ = 13.33

           Standard deviation = $\sqrt{\frac{(13-13.33)^{2} +(10-13.33)^{2} + (17-13.33)^{2} }{3-1} }$ = 3.512

           C.V. =   $\frac{Standard deviation}{Mean} * 100$ = $\frac{3.512}{13.33} * 100$ = 26.35%

Therefore, students of Class A has more variation in weights.