   # Imagine that you and four of your classmates have measured the viscosity of engine oil and recorded the values shown in the accompanying figure. Determine the average, variance, and standard deviation for the measured viscosity of oil. Viscosity of Engine Oil (N.s/m 2 ) 0.15 0.10 0.12 0.11 0.14 ### Engineering Fundamentals: An Intro...

5th Edition
Saeed Moaveni
Publisher: Cengage Learning
ISBN: 9781305084766

#### Solutions

Chapter
Section ### Engineering Fundamentals: An Intro...

5th Edition
Saeed Moaveni
Publisher: Cengage Learning
ISBN: 9781305084766
Chapter 19, Problem 17P
Textbook Problem
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## Imagine that you and four of your classmates have measured the viscosity of engine oil and recorded the values shown in the accompanying figure. Determine the average, variance, and standard deviation for the measured viscosity of oil. Viscosity of Engine Oil (N.s/m2) 0.15 0.10 0.12 0.11 0.14

To determine

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

### Explanation of Solution

Given data:

The given measured values of viscosity of oil are shown below.

 Viscosity of Engine oil (N⋅sm2) 0.15 0.1 0.12 0.11 0.14

The total number of measured values, n=5.

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:

Substitute all the value of viscosity of oil for xi up to the range n, and 5 for n in equation (1) to calculate mean (x¯),

x¯=0.15+0.10+0.12+0.11+0.145=0.625x¯=0

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