ENGINEERING FUNDAMENTALS
ENGINEERING FUNDAMENTALS
6th Edition
ISBN: 9781337705011
Author: MOAVENI
Publisher: CENGAGE L
bartleby

Concept explainers

bartleby

Videos

Textbook Question
Book Icon
Chapter 19, Problem 3P

For Problem 19.1, using Equations (19.1) and (19.6), calculate the mean and standard deviation of the class scores.

Expert Solution & Answer
Check Mark
To determine

Calculate the mean and standard deviation of the class scores.

Answer to Problem 3P

The mean and standard deviation of class scores are 73.2 and 12.5 respectively.

Explanation of Solution

Given data:

The required data are given below with reference to the problem 19.1 in the textbook.

Number of students, n=30.

Students test scores are 57, 94, 81, 77, 66, 97, 62, 86, 75, 87, 91, 78, 61, 82, 74, 72, 70, 88, 66, 75, 55, 66, 58, 73, 79, 51, 63, 77, 52, 84.

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

s=i=1n(xix¯)2n1 (2)

Calculation:

Substitute all the value of student scores for xi up to the range n, and 30 for n in equation (1) to calculate mean (x¯),

x¯=57+94+81+77+66+97+62+86+75+87+91+78+61+82+74+72+70+88+66+75+55+66+58+73+79+51+63+77+52+8430=219730x¯=73.2

Find the terms i=1n(xix¯)2 in the equation (2) as by substituting all the value of student scores for xi up to the range n, 73.2 for x¯ as,

i=1n(xix¯)2=((5773.2)2+(9473.2)2+(8173.2)2+(7773.2)2+(6673.2)2+(9773.2)2+(6273.2)2+(8673.2)2+(7573.2)2+(8773.2)2+(9173.2)2+(7873.2)2+(6173.2)2+(8273.2)2+(7473.2)2+(7273.2)2+(7073.2)2+(8873.2)2+(6673.2)2+(7573.2)2+(5573.2)2+(6673.2)2+(5873.2)2+(7373.2)2+(7973.2)2+(5173.2)2+(6373.2)2+(7773.2)2+(5273.2)2+(8473.2)2)

i=1n(xix¯)2=4531.25

Substitute all the value 4531.25 for i=1n(xix¯)2 and 30 for n in equation (2) to find standard deviation (s),

s=4531.25301s=4531.2529s=156.25s=12.5

Therefore, the mean and standard deviation of class scores are 73.2 and 12.5 respectively.

Conclusion:

Thus, the mean and standard deviation of class scores are 73.2 and 12.5 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
A population has a mean of u=30 and a standard deviation of sd=5. a. If 5 points were added to every score in the population, what would be the new values for the mean and standard deviation? b. If every score in the population were multiplied by 3, what would be the new values for the mean and standard deviation?
can u please answer from d to g thank you
For Problem 19.39 , determine the probability (assuming normal distribution) that a tire could be used reliably for less than 45,000 kilometers.
Knowledge Booster
Background pattern image
Civil Engineering
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, civil-engineering and related others by exploring similar questions and additional content below.
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
What Is A Construction Takeoff? | Are They Still Necessary In Quantity Surveying?; Author: Metroun Quantity Surveying;https://www.youtube.com/watch?v=uTWoDPtcOjg;License: Standard Youtube License