Answered: According to the U.S. Census Bureau,…

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

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.5: Comparing Sets Of Data

Problem 1GP

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Question

According to the U.S. Census Bureau, the distribution of family sizes in the United States for the year 2010 is as shown below.

Number of person	Number of families (thousands)	Percentage of families
2	31455	44.3
3	16073	22.9
4	14496	20.0
5	6526	8.6
6	2246	2.8
7	1249	1.4

That is, 44.3% of the families in the United States have two members, whereas only 2.8% have six members.

(a) Find the mean family size, approximately, from this distribution of family sizes. (b) Find the approximate standard deviation of the family sizes.

(c) Suppose Adam randomly selects 400 families from this population. Describe, as closely as you can, the shape, center, and spread of the 400 data values that might occur in the sample

(d) Adam is actually interested in the mean number of persons per family in samples of

400 families. Describe, as closely as you can, the shape, center, and spread of the distribution of possible values of the sample mean in random samples of 400 families.

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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