Answered: Samples of Size 2 Samples of Size 5…

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

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.3: Measures Of Spread

Problem 1GP

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Question

Waist size A study measured the Waist Size of 250
men, finding a mean of 36.33 inches and a standard
deviation of 4.02 inches. Here is a histogram of these
measurements

a) Describe the histogram of Waist Size.
b) To explore how the mean might vary from sample to
sample, they simulated by drawing many samples of
size 2, 5, 10, and 20, with replacement, from the 250
measurements. Here are histograms of the sample means

for each simulation. Explain how these histograms dem-
onstrate what the Central Limit Theorem says about the

sampling distribution model for sample means.

Samples of Size 2
Samples of Size 5
1400
1000
1200
1000
800
800
600
600
400
400
200
200
30
40
50
30
44
Sample Mean Waist Size (inches)
Sample Mean Waist Size (inches)
Samples of Size 10
Samples of Size 20
1500
2000
1000
1500
1000
500
500
32
36
40
34
40
Sample Mean Waist Size (inches)
Sample Mean Waist Size (inches)
Number of Samples
Number of Samples
Number of Samples
Number of Samples

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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