Answer:
a) Coefficient of Variation for Height = 4.46%
b) Coefficient of Variation for Ages
= 12.26%
c)Comparing both Variations, the coefficient of variation for ages is larger than that of the mean and this is due to the fact that the
Step-by-step explanation:
Coefficient of Variation formula = Standard deviation / Mean × 100%
From the attached diagram, we are given sample data
1) For the Height
a) Mean of the Heights
= Sum of term/ Number of terms
= 74 + 70 + 70 + 76 + 77 + 72 + 75+ 70 + 70 + 80 + 75 + 75/12
= 884/12
= 73.66666667
b) Standard Deviation of Heights
For Sample data, the formula
=√ (X - Mean)²/n - 1
= 3.284490644
c) Coefficient of variation for Heights
Coefficient of Variation formula = Standard deviation / Mean × 100%
=( 3.284490644/73.66666667) × 100
= 0.04458584584 × 100
= 4.45858458441%
≈ 4.46%
2) Mean of ages
= Sum of terms/ Number of terms
= 21 + 26 + 22 + 27 + 29 + 26 + 27 + 29 + 30 + 31 + 31 + 31/12
= 330/12
= 27.5
b)Standard Deviation of Ages
For Sample data, the formula
=√ (X - Mean)²/n - 1
= √ (21 - 27.5)² + (26- 27.5)² +( 22- 27.5)² + (27- 27.5)² + (29- 27.5)² +( 26- 27.5)² +( 27- 27.5)² + (29- 27.5)² + (30 - 27.5)² + (31- 27.5)² + (31- 27.5)²+ (31- 27.5)²/12
=√ -6.5² + -1.5² + -5.5²+ -0.5² + 1.5² + -1.5² + -0.5² + 1.5² + 2.5² +3.5² + 3.5² + 3.5²/ 11
= √125/11
= √11.36363636
= 3.370999312
c) Coefficient of Variation
= Coefficient of Variation formula = Standard deviation / Mean × 100%
= (3.370999312/27.5) × 100
= 0.12258179316 × 100
= 12.258179316%
