Concept explainers
Find the average, variance, and standard deviation for the height, age, and mass of a basketball team.
Answer to Problem 12P
The average height is
The variance of height is
The standard deviation of height is
The average mass is
The variance of mass is
The standard deviation of mass is
The average age is
The variance of age is
The standard deviation of age is
Explanation of Solution
Consider Golden state warriors (GSW) basketball team for the analysis.
Tabulate the details collected from the GSW team as in Table 1.
Players | Age (years) | height (cm) | mass (kg) |
1 | 28 | 201 | 97.5 |
2 | 30 | 206 | 108.9 |
3 | 30 | 190 | 86.2 |
4 | 28 | 211 | 122.5 |
5 | 24 | 206 | 101.6 |
6 | 35 | 198 | 97.5 |
7 | 25 | 188 | 81.2 |
8 | 22 | 206 | 99.8 |
9 | 33 | 201 | 87.1 |
10 | 26 | 203 | 97.5 |
11 | 23 | 201 | 112.9 |
12 | 26 | 198 | 95.3 |
Find the average
Here, the data points are
The number of observations is 12.
Find the variance (v) using the equation.
Find the standard deviation (s) using the equation.
Height:
Calculate the values to find the average, variance, and standard deviation as in Table 2.
S No | height (cm) | ||
1 | 201 | 0.25 | 0.0625 |
2 | 206 | 5.25 | 27.5625 |
3 | 190 | –10.75 | 115.563 |
4 | 211 | 10.25 | 105.063 |
5 | 206 | 5.25 | 27.5625 |
6 | 198 | –2.75 | 7.5625 |
7 | 188 | –12.75 | 162.563 |
8 | 206 | 5.25 | 27.5625 |
9 | 201 | 0.25 | 0.0625 |
10 | 203 | 2.25 | 5.0625 |
11 | 201 | 0.25 | 0.0625 |
12 | 198 | –2.75 | 7.5625 |
Refer the Table 2 for the calculation values.
Substitute 2409 cm for
Therefore, the average height is
Substitute 486.25 cm2 for
Therefore, the variance of height is
Substitute 486.25 cm2 for
Therefore, the standard deviation of height is
Mass:
Calculate the values to find the average, variance, and standard deviation as in Table 3.
S No | mass (kg) | ||
1 | 97.5 | –1.5 | 2.25 |
2 | 108.9 | 9.9 | 98.01 |
3 | 86.2 | –12.8 | 163.84 |
4 | 122.5 | 23.5 | 552.25 |
5 | 101.6 | 2.6 | 6.76 |
6 | 97.5 | –1.5 | 2.25 |
7 | 81.2 | –17.8 | 316.84 |
8 | 99.8 | 0.8 | 0.64 |
9 | 87.1 | –11.9 | 141.61 |
10 | 97.5 | –1.5 | 2.25 |
11 | 112.9 | 13.9 | 193.21 |
12 | 95.3 | –3.7 | 13.69 |
Refer to Table 2 for the calculation values.
Substitute 1188 kg for
Therefore, the average mass is
Substitute 1493.6 kg2 for
Therefore, the variance of mass is
Substitute 1493.6 kg2 for
Therefore, the standard deviation of mass is
Age:
Calculate the values to find the average, variance, and standard deviation as in Table 4.
S No | Age (years) | ||
1 | 28 | 0.5 | 0.25 |
2 | 30 | 2.5 | 6.25 |
3 | 30 | 2.5 | 6.25 |
4 | 28 | 0.5 | 0.25 |
5 | 24 | –3.5 | 12.25 |
6 | 35 | 7.5 | 56.25 |
7 | 25 | –2.5 | 6.25 |
8 | 22 | –5.5 | 30.25 |
9 | 33 | 5.5 | 30.25 |
10 | 26 | –1.5 | 2.25 |
11 | 23 | –4.5 | 20.25 |
12 | 26 | –1.5 | 2.25 |
Refer the Table 2 for the calculation values.
Substitute 330 years for
Therefore, the average age is
Substitute 173 (years)2 for
Therefore, the variance of age is
Substitute 173 (years)2 for
Therefore, the standard deviation of age is
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