Calculate the mean, standard deviation, and variance for the given measured values.
Answer to Problem 9P
The mean, variance, and standard deviation for the given values of lumber width are
The mean, variance, and standard deviation for the given values of steel spherical balls are
Explanation of Solution
Given data:
The given measured values of lumber width and steel spherical balls are shown below.
Lumber Width (in.) | Steel spherical balls (cm) |
3.50 | 1.00 |
3.55 | 0.95 |
2.55 | 1.05 |
3.60 | 1.10 |
3.55 | 1.00 |
3.40 | 0.90 |
3.40 | 0.85 |
3.65 | 1.05 |
3.35 | 0.95 |
3.60 | 0.90 |
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 Lumber width:
Substitute all the value of lumber width for
Substitute all the value of lumber width for
Substitute all the value of lumber width for
Calculation for steel spherical balls:
Substitute all the value of spherical balls for
Substitute all the value of spherical balls for
Substitute all the value of spherical balls for
Therefore, the mean, variance, and standard deviation for the given values of lumber width are
Conclusion:
Thus, the mean, variance, and standard deviation for the given values of lumber width are
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Chapter 19 Solutions
ENGINEERING FUNDAMENTALS/MINDTAP
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