The following data represent the weekly salary of 10 people. Complete parts (a) through (e) below. 260 370 670 860 990 260 260 370 370 260 Question content area bottom Part 1 a. Obtain the sample mean and sample standard deviation of the (ungrouped) data set. x=enter your response here Part 2 sx=enter your response here (Round to one decimal place as needed.) Part 3 b. A frequency distribution for the data, using single-value grouping, is presented in the first two columns of the following table. The third column of the table is for the xf-values. Complete the missing entries in the table and then use the grouped-data formula to obtain the sample mean. Salary x Frequency f Salary•Frequency xf 260 4 1,040 370 3 enter your response here 670 1 enter your response here 860 1 enter your response here 990 1 enter your response here Part 4 Obtain the sample mean. x=enter your response here Part 5 c. Explain why the grouped-data formula always yields the actual sample mean when the data are grouped by using single-value grouping. A. The sum of the xf values Σxi•fi for the grouped-data is equal to the actual mean (x). B. The sum of the xf values Σxi•fi for the grouped-data is equal to the sum of data (Σxi) for the non grouped-data. C. The sum of the xf values Σxi•fi for the grouped-data is equal to the actual standard deviation (sx). D. The sample means are not the same. Part 6 d. Complete the table, then use the table and the grouped-data formula to obtain the sample standard deviation. Salary x Frequency f Deviation from mean x−x Squared deviation x−x2 Squared deviation•Frequency x−x2•f 260 4 enter your response here enter your response here enter your response here 370 3 enter your response here enter your response here enter your response here 670 1 enter your response here enter your response here enter your response here

The following data represent the weekly salary of 10 people. Complete parts (a) through (e) below. 260 370 670 860 990 260 260 370 370 260 Question content area bottom Part 1 a. Obtain the sample mean and sample standard deviation of the (ungrouped) data set. x=enter your response here Part 2 sx=enter your response here (Round to one decimal place as needed.) Part 3 b. A frequency distribution for the data, using single-value grouping, is presented in the first two columns of the following table. The third column of the table is for the xf-values. Complete the missing entries in the table and then use the grouped-data formula to obtain the sample mean. Salary x Frequency f Salary•Frequency xf 260 4 1,040 370 3 enter your response here 670 1 enter your response here 860 1 enter your response here 990 1 enter your response here Part 4 Obtain the sample mean. x=enter your response here Part 5 c. Explain why the grouped-data formula always yields the actual sample mean when the data are grouped by using single-value grouping. A. The sum of the xf values Σxi•fi for the grouped-data is equal to the actual mean (x). B. The sum of the xf values Σxi•fi for the grouped-data is equal to the sum of data (Σxi) for the non grouped-data. C. The sum of the xf values Σxi•fi for the grouped-data is equal to the actual standard deviation (sx). D. The sample means are not the same. Part 6 d. Complete the table, then use the table and the grouped-data formula to obtain the sample standard deviation. Salary x Frequency f Deviation from mean x−x Squared deviation x−x2 Squared deviation•Frequency x−x2•f 260 4 enter your response here enter your response here enter your response here 370 3 enter your response here enter your response here enter your response here 670 1 enter your response here enter your response here enter your response here

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question content area bottom

Part 1

a. Obtain the sample mean and sample standard deviation of the (ungrouped) data set.

x=enter your response here

Part 2

sx=enter your response here

(Round to one decimal place as needed.)

Part 3

b. A frequency distribution for the data, using single-value grouping, is presented in the first two columns of the following table. The third column of the table is for the xf-values. Complete the missing entries in the table and then use the grouped-data formula to obtain the sample mean.

Salary x	Frequency f	Salary•Frequency xf
260	4	1,040
370	3	enter your response here
670	1	enter your response here
860	1	enter your response here
990	1	enter your response here

Part 4

Obtain the sample mean.

x=enter your response here

Part 5

c. Explain why the grouped-data formula always yields the actual sample mean when the data are grouped by using single-value grouping.

The sum of the xf values

Σxi•fi

for the grouped-data is equal to the actual mean

(x).

The sum of the xf values

Σxi•fi

for the grouped-data is equal to the sum of data

(Σxi)

for the non grouped-data.

The sum of the xf values

Σxi•fi

for the grouped-data is equal to the actual standard deviation

(sx).

The sample means are not the same.

Part 6

d. Complete the table, then use the table and the grouped-data formula to obtain the sample standard deviation.

Salary x	Frequency f	Deviation from mean x−x	Squared deviation x−x2	Squared deviation•Frequency x−x2•f
260	4	enter your response here	enter your response here	enter your response here
370	3	enter your response here	enter your response here	enter your response here
670	1	enter your response here	enter your response here	enter your response here
860	1	enter your response here	enter your response here	enter your response here
990	1	enter your response here	enter your response here	enter your response here

Part 7

sx=enter your response here

(Round to one decimal place as needed.)

Part 8

e. Explain why the grouped-data formula always yields the actual sample standard deviation when the data are grouped by using single-value grouping.

The sum of the squared deviations times the frequency

Σxi−x2fi

for the group-data formula is equal to the sample mean of the data

(x).

The sum of the squared deviations times the frequency

Σxi−x2fi

for the group-data formula is equal to the sum of the squared deviations

Σxi−x2

for the non grouped-data.

The sum of the squared deviations times the frequency

Σxi−x2fi

for the group-data formula is equal to the actual sample standard deviation

(sx).

The two sample standard deviations are different.

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 + ...

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