Chapter 14, Problem 11E

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Answer 1

Question

Chapter 14, Problem 11E

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

Expert Solution & Answer

To determine

Whether the mean or the median would be better for the student if the three recorded grades were 99, 88, 95 or if the grades were 99, 70, 77.

Answer to Problem 11E

Solution:

The median would be better for the student.

Explanation of Solution

The given data is,

A=99, 88, 95B=99, 70, 77

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 99,88,95 for x1,x2,x3 respectively in the formula.

Here number of data in the given data set is 3, substitute 3 for n in the formula.

Mean(x¯)=x1+x2+...+xnn=99+88+953=94

Mean of A is 94.

Substitute 99, 70, 77 for x1,x2,x3 respectively in the formula.

Mean(x¯)=x1+x2+...+xnn=99+70+773=82

Mean of B is 82.

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

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

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

Arrange the given data in increasing order.

A=88, 95, 99B=70, 77, 99

Number of values in data set is 3, it is even.

Substitute 3 for n in the formula for odd number of data set A.

Median=(n+12)th value=(3+12)th value=2nd value=95

The median of A is 95.

Substitute 3 for n in the formula for odd number of data set B.

Median=(n+12)th value=(3+12)th value=2nd value=77

The median of B is 77.

Since, mean deviation about mean is zero, whereas, mean deviation about median is minimum. Hence, median would be better for the student.

MATLAB Code:

A = [99 88 95];

B = [99 70 77];

mean_A = mean(A)

mean_B = mean(B)

median_A = median(A)

median_B = median(B)

Save the MATLAB script with the name, Chapter14_54793_14_11E.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 11E

Therefore, the required program is stated above.

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Answer 2

Question

Chapter 14, Problem 11E

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

Expert Solution & Answer

To determine

Whether the mean or the median would be better for the student if the three recorded grades were 99, 88, 95 or if the grades were 99, 70, 77.

Answer to Problem 11E

Solution:

The median would be better for the student.

Explanation of Solution

The given data is,

A=99, 88, 95B=99, 70, 77

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 99,88,95 for x1,x2,x3 respectively in the formula.

Here number of data in the given data set is 3, substitute 3 for n in the formula.

Mean(x¯)=x1+x2+...+xnn=99+88+953=94

Mean of A is 94.

Substitute 99, 70, 77 for x1,x2,x3 respectively in the formula.

Mean(x¯)=x1+x2+...+xnn=99+70+773=82

Mean of B is 82.

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

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

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

Arrange the given data in increasing order.

A=88, 95, 99B=70, 77, 99

Number of values in data set is 3, it is even.

Substitute 3 for n in the formula for odd number of data set A.

Median=(n+12)th value=(3+12)th value=2nd value=95

The median of A is 95.

Substitute 3 for n in the formula for odd number of data set B.

Median=(n+12)th value=(3+12)th value=2nd value=77

The median of B is 77.

Since, mean deviation about mean is zero, whereas, mean deviation about median is minimum. Hence, median would be better for the student.

MATLAB Code:

A = [99 88 95];

B = [99 70 77];

mean_A = mean(A)

mean_B = mean(B)

median_A = median(A)

median_B = median(B)

Save the MATLAB script with the name, Chapter14_54793_14_11E.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 11E

Therefore, the required program is stated above.

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 3

Question

Chapter 14, Problem 11E

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

Expert Solution & Answer

To determine

Whether the mean or the median would be better for the student if the three recorded grades were 99, 88, 95 or if the grades were 99, 70, 77.

Answer to Problem 11E

Solution:

The median would be better for the student.

Explanation of Solution

The given data is,

A=99, 88, 95B=99, 70, 77

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 99,88,95 for x1,x2,x3 respectively in the formula.

Here number of data in the given data set is 3, substitute 3 for n in the formula.

Mean(x¯)=x1+x2+...+xnn=99+88+953=94

Mean of A is 94.

Substitute 99, 70, 77 for x1,x2,x3 respectively in the formula.

Mean(x¯)=x1+x2+...+xnn=99+70+773=82

Mean of B is 82.

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

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

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

Arrange the given data in increasing order.

A=88, 95, 99B=70, 77, 99

Number of values in data set is 3, it is even.

Substitute 3 for n in the formula for odd number of data set A.

Median=(n+12)th value=(3+12)th value=2nd value=95

The median of A is 95.

Substitute 3 for n in the formula for odd number of data set B.

Median=(n+12)th value=(3+12)th value=2nd value=77

The median of B is 77.

Since, mean deviation about mean is zero, whereas, mean deviation about median is minimum. Hence, median would be better for the student.

MATLAB Code:

A = [99 88 95];

B = [99 70 77];

mean_A = mean(A)

mean_B = mean(B)

median_A = median(A)

median_B = median(B)

Save the MATLAB script with the name, Chapter14_54793_14_11E.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 11E

Therefore, the required program is stated above.

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 4

Question

Chapter 14, Problem 11E

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

Expert Solution & Answer

To determine

Whether the mean or the median would be better for the student if the three recorded grades were 99, 88, 95 or if the grades were 99, 70, 77.

Answer to Problem 11E

Solution:

The median would be better for the student.

Explanation of Solution

The given data is,

A=99, 88, 95B=99, 70, 77

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 99,88,95 for x1,x2,x3 respectively in the formula.

Here number of data in the given data set is 3, substitute 3 for n in the formula.

Mean(x¯)=x1+x2+...+xnn=99+88+953=94

Mean of A is 94.

Substitute 99, 70, 77 for x1,x2,x3 respectively in the formula.

Mean(x¯)=x1+x2+...+xnn=99+70+773=82

Mean of B is 82.

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

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

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

Arrange the given data in increasing order.

A=88, 95, 99B=70, 77, 99

Number of values in data set is 3, it is even.

Substitute 3 for n in the formula for odd number of data set A.

Median=(n+12)th value=(3+12)th value=2nd value=95

The median of A is 95.

Substitute 3 for n in the formula for odd number of data set B.

Median=(n+12)th value=(3+12)th value=2nd value=77

The median of B is 77.

Since, mean deviation about mean is zero, whereas, mean deviation about median is minimum. Hence, median would be better for the student.

MATLAB Code:

A = [99 88 95];

B = [99 70 77];

mean_A = mean(A)

mean_B = mean(B)

median_A = median(A)

median_B = median(B)

Save the MATLAB script with the name, Chapter14_54793_14_11E.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 11E

Therefore, the required program is stated above.

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!

Answer 5

Expert Solution & Answer

To determine

Whether the mean or the median would be better for the student if the three recorded grades were 99, 88, 95 or if the grades were 99, 70, 77.

Answer to Problem 11E

Solution:

The median would be better for the student.

Explanation of Solution

The given data is,

A=99, 88, 95B=99, 70, 77

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 99,88,95 for x1,x2,x3 respectively in the formula.

Here number of data in the given data set is 3, substitute 3 for n in the formula.

Mean(x¯)=x1+x2+...+xnn=99+88+953=94

Mean of A is 94.

Substitute 99, 70, 77 for x1,x2,x3 respectively in the formula.

Mean(x¯)=x1+x2+...+xnn=99+70+773=82

Mean of B is 82.

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

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

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

Arrange the given data in increasing order.

A=88, 95, 99B=70, 77, 99

Number of values in data set is 3, it is even.

Substitute 3 for n in the formula for odd number of data set A.

Median=(n+12)th value=(3+12)th value=2nd value=95

The median of A is 95.

Substitute 3 for n in the formula for odd number of data set B.

Median=(n+12)th value=(3+12)th value=2nd value=77

The median of B is 77.

Since, mean deviation about mean is zero, whereas, mean deviation about median is minimum. Hence, median would be better for the student.

MATLAB Code:

A = [99 88 95];

B = [99 70 77];

mean_A = mean(A)

mean_B = mean(B)

median_A = median(A)

median_B = median(B)

Save the MATLAB script with the name, Chapter14_54793_14_11E.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 11E

Therefore, the required program is stated above.

Answer 6

Expert Solution & Answer

To determine

Whether the mean or the median would be better for the student if the three recorded grades were 99, 88, 95 or if the grades were 99, 70, 77.

Answer to Problem 11E

Solution:

The median would be better for the student.

Explanation of Solution

The given data is,

A=99, 88, 95B=99, 70, 77

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 99,88,95 for x1,x2,x3 respectively in the formula.

Here number of data in the given data set is 3, substitute 3 for n in the formula.

Mean(x¯)=x1+x2+...+xnn=99+88+953=94

Mean of A is 94.

Substitute 99, 70, 77 for x1,x2,x3 respectively in the formula.

Mean(x¯)=x1+x2+...+xnn=99+70+773=82

Mean of B is 82.

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

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

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

Arrange the given data in increasing order.

A=88, 95, 99B=70, 77, 99

Number of values in data set is 3, it is even.

Substitute 3 for n in the formula for odd number of data set A.

Median=(n+12)th value=(3+12)th value=2nd value=95

The median of A is 95.

Substitute 3 for n in the formula for odd number of data set B.

Median=(n+12)th value=(3+12)th value=2nd value=77

The median of B is 77.

Since, mean deviation about mean is zero, whereas, mean deviation about median is minimum. Hence, median would be better for the student.

MATLAB Code:

A = [99 88 95];

B = [99 70 77];

mean_A = mean(A)

mean_B = mean(B)

median_A = median(A)

median_B = median(B)

Save the MATLAB script with the name, Chapter14_54793_14_11E.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 11E

Therefore, the required program is stated above.

Answer 7

Expert Solution & Answer

Answer 8

Expert Solution & Answer

Answer 9

To determine

Whether the mean or the median would be better for the student if the three recorded grades were 99, 88, 95 or if the grades were 99, 70, 77.

Answer 10

Answer to Problem 11E

Solution:

The median would be better for the student.

Answer 11

Explanation of Solution

The given data is,

A=99, 88, 95B=99, 70, 77

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 99,88,95 for x1,x2,x3 respectively in the formula.

Here number of data in the given data set is 3, substitute 3 for n in the formula.

Mean(x¯)=x1+x2+...+xnn=99+88+953=94

Mean of A is 94.

Substitute 99, 70, 77 for x1,x2,x3 respectively in the formula.

Mean(x¯)=x1+x2+...+xnn=99+70+773=82

Mean of B is 82.

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

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

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

Arrange the given data in increasing order.

A=88, 95, 99B=70, 77, 99

Number of values in data set is 3, it is even.

Substitute 3 for n in the formula for odd number of data set A.

Median=(n+12)th value=(3+12)th value=2nd value=95

The median of A is 95.

Substitute 3 for n in the formula for odd number of data set B.

Median=(n+12)th value=(3+12)th value=2nd value=77

The median of B is 77.

Since, mean deviation about mean is zero, whereas, mean deviation about median is minimum. Hence, median would be better for the student.

MATLAB Code:

A = [99 88 95];

B = [99 70 77];

mean_A = mean(A)

mean_B = mean(B)

median_A = median(A)

median_B = median(B)

Save the MATLAB script with the name, Chapter14_54793_14_11E.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 11E

Therefore, the required program is stated above.