Respuesta :
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%
Compare the variation in heights to the variation in weights of thirteen-year old girls is :
- Height = 4.3%
- Weight = 16.8%
There is substantially more variation in the weights than in the heights of the girls.
Given Information :
- 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
For the heights,
Mean height = (Σx)/N
- 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
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)
Variation in terms of the mean = 0.0429
Variation in terms of the mean= 4.3%.
For the weights,
Mean weight = (Σx)/N
- x = each weight
- N = number of girls sampled = 9
- Mean weight = (89+97+93+119+96+90+123+98+139)/9
- Mean weight = (944/9)
- Mean weight = 104.9 pounds
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)
Variation in terms of the mean = 0.168
Variation in terms of the mean = 16.8%
Thus, there is substantially more variation in the weights than in the heights of the girls.
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