Answered: The frequency distribution was obtained…

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

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter4: Equations Of Linear Functions

Section4.6: Regression And Median-fit Lines

Problem 1AGP

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Question

The frequency distribution was obtained using a class width of

0.5

for data on cigarette tax rates. Use the frequency distribution to approximate the population mean and population standard deviation. Compare these results to the actual mean

μ=$1.956

and standard deviation

σ=$1.236.

Click the icon to view the frequency distribution for the tax rates.

The population mean is

$nothing.

(Round to three decimal places as needed.)

The population standard deviation is

$nothing.

(Round to three decimal places as needed.)

Compare these results to the values found using the actual data.

The grouped values are both slightly larger.

The grouped mean is slightly smaller, while the grouped standard deviation is slightly larger.

The grouped mean is slightly larger, while the grouped standard deviation is slightly smaller.

The grouped values are both slightly smaller.

Click to select your answer(s).

Frequency distribution of cigarette tax rates

Tax Rate		frequecy
0.00–	0.49	6
0.50–	0.99	15
1.00–	1.49	6
1.50–	1.99	6
2.00–	2.49	6
2.50–	2.99	6
3.00–	3.49	6
3.50–	3.99	6
4.00–	4.49	5

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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