Chapter 1: Q. 84. (page 53)

When comparing two distributions, it would be best to use relative frequency histograms rather than frequency histograms when
a. the distributions have different shapes.
b. the distributions have different amounts of variability.
c. the distributions have different centers.
d. the distributions have different numbers of observations.
e. at least one of the distributions has outliers

Short Answer

Expert verified

The correct option is (d)

d. the distributions have different numbers of observations.

Step by step solution

Given information.

When comparing two distributions.

a. the distributions have different shapes.

b. the distributions have different amounts of variability.

c. the distributions have different centers.

d. the distributions have different numbers of observations.

e. at least one of the distributions has outliers

Step 2. When analysing data, relative frequency histograms should be used rather than frequency histograms.

(a) Because the shape of the distributions will be the same in a relative frequency histogram and a frequency histogram, we do not prefer the relative frequency histogram over the frequency histogram (as we learn the same information from both histograms).

(b) The spread of the distributions in a relative frequency histogram and a frequency histogram will be the same because the width of the histograms will be the same. Thus, if the spreads of the distributions differ, we do not prefer the relative frequency histogram over the frequency histogram (as we learn the same information from both histograms).

(c) The center of the distributions in a relative frequency histogram and a frequency histogram will be the same because the highest bars in both histograms will be the same. Thus, if the distributions have different centers, the relative frequency histogram is not preferred over the frequency histogram (as we learn the same information from both histograms).

(d) If the distributions have a different number of observations, a relative frequency histogram is preferable to a frequency histogram. For example, if one data set has 10,000 observations and the other data set has only 100 observations, comparing the distributions in a frequency histogram is nearly impossible because the histogram corresponding to the 10,000 observations will have much higher bars than the histogram corresponding to the 100 observations (thus the histogram of the 100 observations will be extremely small when the two histograms are drawn on the same scale, which makes it nearly impossible to see the distribution of the 100 observations).

(e) If at least one of the distributions contains outliers, we do not prefer the relative frequency histogram over the frequency histogram because both will reveal the presence of the outliers.

As a result:

(d) Different number of observations