Answered: a) Obtain the mean and standard…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section: Chapter Questions

Problem 4SGR

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Question

a) Obtain the mean and standard deviation for WKWEHR_C for the overall full sample (our population of interest).

How close is the mean work hours to the average mean work hours based on your 8 samples? How close is the SD to the calculated mean of the SD_ WKWEHR_C of your 8 samples?
Are answers in a & b what you expected? Does this surprise you in any way?

b) If you continued to take 5% samples from this same “population” another 50 times and then recalculated the overall mean work hours and the average standard deviation of work hours of the samples, do you think these numbers would stay the same as calculated above or change? If you think they would change, explain in what way.

Number of hours usually worked at
all jobs in a week.
N
Valid
1334
Missing
857
Mean
38.838
Std. Deviation
13.8724
Minimum
.3
Maximum
75.0

Sample #
Sample_Size
(N)
Min_
Маx_
Mean_
SD_
WKWEHR_C
WKWEHR_C
WKWEHR_C
WKWEHR_C
1
66
2
75
39.01
14.58
2
57
75
39.04
15.79
3
67
12
75
41.37
12.82
4
75
4
75
40.20
13.99
67
75
42.75
15.50
6.
72
2
75
38.93
14.30
7
70
2
75
37.50
14.38
8
61
75
39.13
13.25
Range
18
10
5.25
2.97
Mean
66.88
4.13
75
39.74
14.33
6.
3.

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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