EP WEBASSIGN FOR MOAVENI'S ENGINEERING
EP WEBASSIGN FOR MOAVENI'S ENGINEERING
6th Edition
ISBN: 9780357126592
Author: MOAVENI
Publisher: CENGAGE CO
Question
Book Icon
Chapter 19, Problem 9P
To determine

Calculate the mean, standard deviation, and variance for the given measured values.

Expert Solution & Answer
Check Mark

Answer to Problem 9P

The mean, variance, and standard deviation for the given values of lumber width are 3.505, 0.010, and 0.101 respectively.

The mean, variance, and standard deviation for the given values of steel spherical balls are 0.975, 0.006, and 0.079 respectively.

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)
3.501.00
3.550.95
2.551.05
3.601.10
3.551.00
3.400.90
3.400.85
3.651.05
3.350.95
3.600.90

The total number of measured values, n=10.

Formula used:

From equation 19.1 in the textbook, the formula to find mean for any sample is,

x¯=x1+x2+x3+............+xn1+xnn=1ni=1nxi (1)

Here,

x¯ is the mean,

xi is the data points,

n is the number of data points.

From equation 19.5 in the textbook, the formula to find the variance is,

v=i=1n(xix¯)2n1 (2)

From equation 19.6 in the textbook, the formula to find standard deviation is,

s=i=1n(xix¯)2n1 (3)

Calculation:

Calculation for Lumber width:

Substitute all the value of lumber width for xi up to the range n, and 10 for n in equation (1) to calculate mean (x¯),

x¯=3.50+3.55+3.45+3.60+3.55+3.40+3.40+3.65+3.35+3.6010=35.0510x¯=3.505

Substitute all the value of lumber width for xi up to the range n, 3.505 for x¯, and 10 for n in equation (2) to find variance (v),

v=(3.503.505)2+(3.553.505)2+(3.453.505)2+(3.603.505)2+(3.553.505)2+(3.403.505)2+(3.403.505)2+(3.653.505)2+(3.353.505)2+(3.603.505)2101=0.092259v=0.010

Substitute all the value of lumber width for xi up to the range n, 3.505 for x¯, and 10 for n in equation (3) to find standard deviation (s),

s=(3.503.505)2+(3.553.505)2+(3.453.505)2+(3.603.505)2+(3.553.505)2+(3.403.505)2+(3.403.505)2+(3.653.505)2+(3.353.505)2+(3.603.505)2101

s=0.092259s=0.010s=0.101

Calculation for steel spherical balls:

Substitute all the value of spherical balls for xi up to the range n, and 10 for n in equation (1) to calculate mean (x¯),

x¯=1.00+0.95+1.05+1.10+1.00+0.90+0.85+1.05+0.95+0.9010=9.7510x¯=0.975

Substitute all the value of spherical balls for xi up to the range n, 0.975 for x¯, and 10 for n in equation (2) to find variance (v),

v=(1.000.975)2+(0.950.975)2+(1.050.975)2+(1.100.975)2+(1.000.975)2+(0.900.975)2+(0.850.975)2+(1.050.975)2+(0.950.975)2+(0.900.975)2101=0.05629v=0.006

Substitute all the value of spherical balls for xi up to the range n, 0.975 for x¯, and 10 for n in equation (3) to find standard deviation (s),

s=(1.000.975)2+(0.950.975)2+(1.050.975)2+(1.100.975)2+(1.000.975)2+(0.900.975)2+(0.850.975)2+(1.050.975)2+(0.950.975)2+(0.900.975)2101=0.05629=0.006s=0.079

Therefore, the mean, variance, and standard deviation for the given values of lumber width are 3.505, 0.010, and 0.101 respectively, and the mean, variance, and standard deviation for the given values of steel spherical balls are 0.975, 0.006, and 0.079 respectively.

Conclusion:

Thus, the mean, variance, and standard deviation for the given values of lumber width are 3.505, 0.010, and 0.101 respectively, and the mean, variance, and standard deviation for the given values of steel spherical balls are 0.975, 0.006, and 0.079 respectively.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Students have asked these similar questions
For each random variable defined here, (i) indicate if it is discrete or continuous, and (ii) write the set of possible values for the variable (e.g., possible values of X are 0
help me with this Question for revision purposes and as well with citation The office building was built in year 2017 and has not obtained any Green Mark certification before. The office building is occupied by a single tenant/entity. The building management team had done an analysis of the building’s energy performance by extracting the data from the various systems. The current performance and findings of the systems are listed in Appendix A. The client is considering to have the building undergo retrofitting to improve the building’s energy performance. The objective is to achieve Green Mark Gold Plus under the new Green Mark 2021 framework. For part (a) below, you are to use Pathway 1: EUI for this. (a) As part of the feasibility exercise, you are to interpret the current performance of the existing building based on the data available (Refer to Appendix A). You should then organise and present to the client how does the current building relate to the Energy Efficiency Section of…
Locate imaginary wells on Figure P7.5.1, which will replace the actual boundaries with an equivalent hydraulic system. Stream a Real well Impermeable boundary
Knowledge Booster
Background pattern image
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
Engineering Fundamentals: An Introduction to Engi...
Civil Engineering
ISBN:9781305084766
Author:Saeed Moaveni
Publisher:Cengage Learning