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Chapter 2: Q 2.19 (page 50)

Answer true or false to each of the statements in parts (a) and (b), and explain your reasoning.

a. Two data sets that have identical frequency distributions have identical relative-frequency distributions.

b. Two data sets that have identical relative-frequency distributions have identical frequency distributions.

c. Use your answers to parts (a) and (b) to explain why relative frequency distributions are better than frequency distributions for comparing two data sets.

Short Answer

Expert verified

a)The statement is true

b)The statement is false

c)When comparing two data sets, the relative frequency distribution is preferable than the frequency distribution since the relative frequency is always between 0 and 1. As a result, it serves as a benchmark for comparison.

Step by step solution

01

Part (a) Step 1: Given Information

We have to explain two data sets that have identical frequency distributions have identical relative-frequency distributions_True or False

02

Part (a) Step 2: Explanation

Take a look at the given statement.

The frequency distributions and relative-frequency distributions of two data sets are equal.

The assertion holds valid while tabulating relative frequency values, as it makes use of frequency table values. As a result, the frequency distributions of the two data sets are identical.

As a result, it makes use of the frequency table values.

03

Part (b) Step 1 : Given Information

We have to explain two data sets that have identical relative-frequency distributions have identical frequency distributions -True or False

04

Part (b) Step 2: Explanation

Take a look at the given statement.

The relative-frequency distributions of two data sets are similar, as are the frequency distributions.

The assertion is erroneous since the total number of observations in the two circumstances can differ. As a result, if two data sets have equal relative-frequency distributions, their frequency distributions are not identical.

As a result, the stated statement is untrue because the total number of observations in the two circumstances can differ.

05

Part (c) Step 1: Given Information

Given that the statement is, Two data sets have identical relative-frequency distributions have identical frequency distributions.

06

Part (c) Step 2: Explanation

When comparing two data sets, the relative frequency distribution is preferable than the frequency distribution since the relative frequency is always between 0 and 1. As a result, it provides a benchmark for comparison, which is not available in the frequency distribution of data.

Because the relative frequency distribution always resides between 0 and 1, it is better than the frequency distribution for comparing two data sets. As a result, it serves as a benchmark for comparison.

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Most popular questions from this chapter

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In this case, decide which type of grouping (single-value, limit, or cutpoint) is probably the best.

Suppose that you have a data set that contains a large number of observations. Which graphical display is generally preferable; a histogram or a stem-and-leaf diagram? Explain your answer.

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