Concept explainers
Calculate the mean, standard deviation, and variance for the given measured values.
Answer to Problem 8P
The mean, variance, and standard deviation for the given values of screw length are
The mean, variance, and standard deviation for the given values of pipe diameter are
Explanation of Solution
Given data:
The given measured values of screw length and pipe diameter are shown below.
Screw Length (cm) | Pipe diameter (in.) |
2.55 | 1.25 |
2.45 | 1.18 |
2.55 | 1.22 |
2.35 | 1.15 |
2.6 | 1.17 |
2.4 | 1.19 |
2.3 | 1.22 |
2.4 | 1.18 |
2.5 | 1.17 |
2.5 | 1.25 |
The total number of measured values,
Formula used:
From equation 19.1 in the textbook, the formula to find mean for any sample is,
Here,
From equation 19.5 in the textbook, the formula to find the variance is,
From equation 19.6 in the textbook, the formula to find standard deviation is,
Calculation:
Calculation for Screw length:
Substitute all the value of screw length for
Substitute all the value of screw length for
Substitute all the value of screw length for
Calculation for pipe diameter:
Substitute all the value of pipe diameter for
Substitute all the value of pipe diameter for
Substitute all the value of pipe diameter for
Therefore, the mean, variance, and standard deviation for the given values of screw length are
Conclusion:
Thus, the mean, variance, and standard deviation for the given values of screw length are
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Chapter 19 Solutions
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