MATLAB: A Practical Introduction to Programming and Problem Solving
MATLAB: A Practical Introduction to Programming and Problem Solving
5th Edition
ISBN: 9780128154793
Author: Stormy Attaway Ph.D. Boston University
Publisher: Elsevier Science
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Chapter 14, Problem 1E
To determine

To find:

The mean, median, mode, and standard deviation using built-in functions.

Expert Solution & Answer
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Answer to Problem 1E

Solution:

The required answers are stated as follows.

Explanation of Solution

The given data is,

Prod.lineA:15.9415.9815.9416.1615.8615.8615.9015.88Prod.lineB:15.9615.9416.0216.1015.9216.0015.9616.02

The formula to calculate the mean of set of data is,

Mean(x¯)=x1+x2+...+xnn=i1nxin

Here, xi is the ith data value and n is the number of data values in the data set.

Substitute 15.94,15.9815.94,...,15.88 for x1,x2,x3,...,x8 respectively in the formula.

Here number of data in the given data set is 8, substitute 8 for n in the formula.

Mean(x¯)=x1+x2+...+xnn=15.94+15.98+15.94+16.16+15.86+15.86+15.90+15.88815.94

Mean of A is 15.94.

Substitute 15.96, 15.94, 16.02,......16.02 for x1,x2,x3,...,x8 respectively in the formula.

Mean(x¯)=x1+x2+...+xnn=15.96+15.94+16.02+16.10+15.92+16.00+15.96+16.02815.99

Mean of B is 15.99.

The formula to calculate the median of set of ordered data is,

Median={(n+12)thvalue,n=odd12[(n2)thvalue+(n+12)thvalue],n=even

n is the number of data values in the data set.

Arrange the given data in increasing order.

Prod.lineA:15.8615.8615.8815.9015.9415.9415.9816.16Prod.lineB:15.9215.9415.9615.9616.0016.0216.0216.10

Number of values in data set is 8, it is even.

Substitute 8 for n in the formula for even number of data set A.

Median=12[(n2)thvalue+(n2+1)thvalue]=12[(82)thvalue+(82+1)thvalue]=12[4thvalue+5thvalue]=12[15.90+15.94]

Simplify further,

Median=12[15.90+15.94]=15.92

The median of A is 15.92.

Substitute 8 for n in the formula for even number of data set B.

Median=12[(n2)thvalue+(n2+1)thvalue]=12[(82)thvalue+(82+1)thvalue]=12[4thvalue+5thvalue]=12[15.96+16.00]

Simplify further,

Median=12[15.96+16.00]=15.98

The median of B is 15.98.

The most frequently occurred data is the mode.

Here, each of the data 15.86 in A occur 2 times.

Mode of the given data set A are 15.86.

Here, each of the data 15.96 in B occur 2 times.

Mode of the given data set B are 15.96.

Since, the mean value of set B is closer to diameter 16mm. Hence, set B is better than set A.

MATLAB Code:

A = [15.94, 15.98, 15.94, 16.16, 15.86, 15.86, 15.90, 15.88];

B = [15.96, 15.94, 16.02, 16.10, 15.92, 16.00, 15.96, 16.02];

mean_A = mean(A)

mean_B = mean(B)

median_A = median(A)

median_B = median(B)

mode_A = mode(A)

mode_B = mode(B)

stdev_A = std(A)

stdev_B = std(B)

Save the MATLAB script with the name, Chapter14_54793_14_1E.m in the current folder. Execute the script by typing the script name at the command window to generate output.

Result:

MATLAB: A Practical Introduction to Programming and Problem Solving, Chapter 14, Problem 1E , additional homework tip  1

MATLAB: A Practical Introduction to Programming and Problem Solving, Chapter 14, Problem 1E , additional homework tip  2

Therefore, the required program is stated above.

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