Question

Compare the variation in heights to the variation in weights of thirteen-year old girls. The heights 17) (in inches) and weights (in pounds) of nine randomly selected thirteen-year old girls are listed below. Heights (inches): 58.7 61.4 62.1 64.7 60.1 58.3 64.6 63.7 66.1 Weights (pounds): 89 97 93 119 96 90 123 98 139 A) Weights: 15.2% There is substantially more variation in the weights than in the heights of the girls. B) Heights: 11.8% There is substantially more variation in the heights than in the weights of the girls. C) Heights: 4.3% Weights: 16.0% There is substantially more variation in the weights than in the heights of the girls. D) Heights: 4.5% Weights: 16.8% There is substantially more variation in the weights than in the heights of the girls.

Answer 1

Answer:

Height = 4.3%

Weight = 16.8%

There is substantially more variation in the weights than in the heights of the girls.

Step-by-step explanation:

The heights of the girls in inches

58.7 61.4 62.1 64.7 60.1 58.3 64.6 63.7 66.1

The weight of the girls in pounds

89 97 93 119 96 90 123 98 139

Before we start calculation for variations, we first find the means

The mean height = (Σx)/N

The average is the sum of variables divided by the number of variables

x = each height

N = number of girls sampled = 9

Mean height = (58.7+61.4+62.1+64.7+60.1+58.3+64.6+63.7+66.1)/9

Mean height = (559.7/9)

Mean height = 62.2 inches

The standard deviation is the square root of variance. And variance is an average of the squared deviations from the mean.

Mathematically,

Standard deviation = σ = √[Σ(x - xbar)²/(N-1)]

x = each variable

xbar = mean = 62.2

N = number of variables

Σ(x - xbar)² = [(58.7-62.2)² + (61.4-62.2)² + (62.1-62.2)² + (64.7-62.2)² + (60.1-62.2)² + (58.3-62.2)² + (64.6-62.2)² + (63.7-62.2)² + (66.1-62.2)²] = 56.94

σ = √(56.94/8) = √(7.1175)

σ = 2.67 inches

Variation in terms of the mean = (2.67/62.2) = 0.0429 = 4.3%.

For the weights,

we first find the means

The mean weight = (Σx)/N

The average is the sum of variables divided by the number of variables

x = each weight

N = number of girls sampled = 9

Mean height = (89+97+93+119+96+90+123+98+139)/9

Mean height = (944/9)

Mean height = 104.9 pounds

The standard deviation is the square root of variance. And variance is an average of the squared deviations from the mean.

Mathematically,

Standard deviation = σ = √[Σ(x - xbar)²/(N-1)]

x = each variable

xbar = mean = 104.9

N = number of variables

Σ(x - xbar)² = [(89-104.9)² + (97-104.9)² + (93-104.9)² + (119-104.9)² + (96-104.9)² + (90-104.9)² + (123-104.9)² + (98-104.9)² + (139-104.9)²] = 2,494.89

σ = √(2,494.89/8) = √(311.86)

σ = 17.66 pounds

Variation in terms of the mean = (17.66/104.9) = 0.168 = 16.8%