NUMERICAL METH. F/ENGR.(LL)--W/ACCESS
NUMERICAL METH. F/ENGR.(LL)--W/ACCESS
7th Edition
ISBN: 9781260514131
Author: Chapra
Publisher: MCG
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Textbook Question
Chapter 17, Problem 1P

Given these data

8.8 9.5 9.8 9.4 10.0
9.4 10.1 9.2 11.3 9.4
10.0 10.4 7.9 10.4 9.8
9.8 9.5 8.9 8.8 10.6
10.1 9.5 9.6 10.2 8.9

Determine

(a) The Mean,

(b) The standard deviation,

(c) The Variance,

(d) The coefficient of variation, and

(e) The 95% confidence interval for the mean

(f) Construct a histogram using a range from 7.5 to 11.5 with intervals of 0.5

(a)

Expert Solution
Check Mark
To determine

To calculate: The mean of the given data.

8.8 9.5 9.8 9.4 10
9.4 10.1 9.2 11.3 9.4
10 10.4 7.9 10.4 9.8
9.8 9.5 8.9 8.8 10.6
10.1 9.5 9.6 10.2 8.9

Answer to Problem 1P

Solution:

The mean of the given data is 9.652.

Explanation of Solution

Given Information:

The data is,

8.8 9.5 9.8 9.4 10
9.4 10.1 9.2 11.3 9.4
10 10.4 7.9 10.4 9.8
9.8 9.5 8.9 8.8 10.6
10.1 9.5 9.6 10.2 8.9

Calculation:

The mean of the data can be found out with the help of excel as shown below,

Step 1. First put the data in the excel as shown below,

NUMERICAL METH. F/ENGR.(LL)--W/ACCESS, Chapter 17, Problem 1P , additional homework tip  1

Step 2. Use AVERAGE command in excel as shown below,

NUMERICAL METH. F/ENGR.(LL)--W/ACCESS, Chapter 17, Problem 1P , additional homework tip  2

Hence, the mean of the given data is 9.652.

(b)

Expert Solution
Check Mark
To determine

To calculate: The standard deviation of the given data.

8.8 9.5 9.8 9.4 10
9.4 10.1 9.2 11.3 9.4
10 10.4 7.9 10.4 9.8
9.8 9.5 8.9 8.8 10.6
10.1 9.5 9.6 10.2 8.9

Answer to Problem 1P

Solution:

The standard deviation of the given data is 0.703041.

Explanation of Solution

Given Information:

The data is,

8.8 9.5 9.8 9.4 10
9.4 10.1 9.2 11.3 9.4
10 10.4 7.9 10.4 9.8
9.8 9.5 8.9 8.8 10.6
10.1 9.5 9.6 10.2 8.9

Calculation:

The standard deviation of the data can be found out with the help of excel as shown below,

Step 1. First put the data in the excel as shown below,

NUMERICAL METH. F/ENGR.(LL)--W/ACCESS, Chapter 17, Problem 1P , additional homework tip  3

Step 2. Use STDEV command in excel as shown below,

NUMERICAL METH. F/ENGR.(LL)--W/ACCESS, Chapter 17, Problem 1P , additional homework tip  4

Hence, the standard deviation of the given data is 0.703041.

(c)

Expert Solution
Check Mark
To determine

To calculate: The variance of the given data.

8.8 9.5 9.8 9.4 10
9.4 10.1 9.2 11.3 9.4
10 10.4 7.9 10.4 9.8
9.8 9.5 8.9 8.8 10.6
10.1 9.5 9.6 10.2 8.9

Answer to Problem 1P

Solution:

The variance of the given data is 0.494267.

Explanation of Solution

Given Information:

The data is,

8.8 9.5 9.8 9.4 10
9.4 10.1 9.2 11.3 9.4
10 10.4 7.9 10.4 9.8
9.8 9.5 8.9 8.8 10.6
10.1 9.5 9.6 10.2 8.9

Calculation:

The variance of the data can be found out with the help of excel as shown below,

Step 1. First put the data in the excel as shown below,

NUMERICAL METH. F/ENGR.(LL)--W/ACCESS, Chapter 17, Problem 1P , additional homework tip  5

Step 2. Use VAR command in excel as shown below,

NUMERICAL METH. F/ENGR.(LL)--W/ACCESS, Chapter 17, Problem 1P , additional homework tip  6

Hence, the variance of the given data is 0.494267.

(d)

Expert Solution
Check Mark
To determine

To calculate: The coefficient of variation of the given data.

8.8 9.5 9.8 9.4 10
9.4 10.1 9.2 11.3 9.4
10 10.4 7.9 10.4 9.8
9.8 9.5 8.9 8.8 10.6
10.1 9.5 9.6 10.2 8.9

Answer to Problem 1P

Solution:

The coefficient of variation of the given data is 7.28%.

Explanation of Solution

Given Information:

The data is,

8.8 9.5 9.8 9.4 10
9.4 10.1 9.2 11.3 9.4
10 10.4 7.9 10.4 9.8
9.8 9.5 8.9 8.8 10.6
10.1 9.5 9.6 10.2 8.9

Formula used:

The coefficient of variation is standarddeviationmean×100%.

Calculation:

The coefficient of variation of the data can be found out with the help of excel as shown below,

Step 1. First put the data in the excel as shown below,

NUMERICAL METH. F/ENGR.(LL)--W/ACCESS, Chapter 17, Problem 1P , additional homework tip  7

Step 2. Use coefficient of variation formula as shown below,

NUMERICAL METH. F/ENGR.(LL)--W/ACCESS, Chapter 17, Problem 1P , additional homework tip  8

Hence, the coefficient of variation of the given data is 7.28%.

(e)

Expert Solution
Check Mark
To determine

To calculate: The 95% confidence interval for the mean of the given data.

8.8 9.5 9.8 9.4 10
9.4 10.1 9.2 11.3 9.4
10 10.4 7.9 10.4 9.8
9.8 9.5 8.9 8.8 10.6
10.1 9.5 9.6 10.2 8.9

Answer to Problem 1P

Solution:

The 95% confidence interval lower and upper value is 9.361799and9.942201.

Explanation of Solution

Given Information:

The data is,

8.8 9.5 9.8 9.4 10
9.4 10.1 9.2 11.3 9.4
10 10.4 7.9 10.4 9.8
9.8 9.5 8.9 8.8 10.6
10.1 9.5 9.6 10.2 8.9

Formula used:

The upper and lower range of 95% confidence interval can be found out by,

L=y¯syn×tα2,n1andU=y¯+syn×tα2,n1

Where y¯ is mean, sy is standard deviation, n id number of data points, α is probability and t is statistics calculator value.

Calculation:

Here, y¯=9.652,sy=0.703041,α=0.05andn=25

The t calculator value for the given values is,

tα2,n1=t0.052,251=t0.025,24=2.064

Use the formula to calculate the lower range,

L=y¯syn×tα2,n1=9.6520.70304125×2.064=9.361799

And the upper range is,

U=y¯+syn×tα2,n1=9.652+0.70304125×2.064=9.942201

Hence, the 95% confidence interval lower and upper value is 9.361799and9.942201.

(f)

Expert Solution
Check Mark
To determine

To graph: The histogram of the given data by using a range from 7.5to11.5 with intervals of 0.5

8.8 9.5 9.8 9.4 10
9.4 10.1 9.2 11.3 9.4
10 10.4 7.9 10.4 9.8
9.8 9.5 8.9 8.8 10.6
10.1 9.5 9.6 10.2 8.9

Explanation of Solution

Given Information:

The data is,

8.8 9.5 9.8 9.4 10
9.4 10.1 9.2 11.3 9.4
10 10.4 7.9 10.4 9.8
9.8 9.5 8.9 8.8 10.6
10.1 9.5 9.6 10.2 8.9

Graph:

The histogram of the data can be found out with the help of excel as shown below,

Step 1. First put the data in the excel as shown below,

NUMERICAL METH. F/ENGR.(LL)--W/ACCESS, Chapter 17, Problem 1P , additional homework tip  9

Step 2. Now insert the bin array range as shown below,

NUMERICAL METH. F/ENGR.(LL)--W/ACCESS, Chapter 17, Problem 1P , additional homework tip  10

Step 3. Select on DATA, Data Analysis, Histogram and then OK.

NUMERICAL METH. F/ENGR.(LL)--W/ACCESS, Chapter 17, Problem 1P , additional homework tip  11

Step 4. Enter the input, Bin and output range as shown below,

NUMERICAL METH. F/ENGR.(LL)--W/ACCESS, Chapter 17, Problem 1P , additional homework tip  12

Step 5. The following result will appear.

NUMERICAL METH. F/ENGR.(LL)--W/ACCESS, Chapter 17, Problem 1P , additional homework tip  13

Step 6. Now click on the insert and then column chart.

Interpretation:

It can be concluded from the histogram that 9.5 has repeated maximum time in the given data.

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Chapter 17 Solutions

NUMERICAL METH. F/ENGR.(LL)--W/ACCESS

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