# construct frequency polygons

2.17 Are there any conspicuous differences between the two distributions in the following table (one reﬂecting the ages of all residents of a small town and the other reﬂecting the ages of all U.S. residents)?

(a) To help make the desired comparison, convert the frequencies ( f ) for the small town to percentages.

(b) Describe any seemingly conspicuous differences between the two distributions.

TWO AGE DISTRIBUTIONS

U.S. POPULATION (2010) (%)13,5,6,7,7,7,7,6,7,7,7,7,7, population Total-100%

AGE 65–above 60-64,55-59,50-54,45-49,40-44,65-39,30-34,25-29,20-24,15-19,

10-14,5-9,0-4

SMALL TOWN f 105,53,45,40,44,38,31,27,25,20,20,19,17,16 TOTAL 500

NOTE: The top class (65–above) has no upper boundary. Although less preferred, as discussed previously, this type of open-ended class is employed as a space-saving device when, as in the Statistical Abstract of the United States, many different tables must be listed. Source: 2012 Statistical Abstract of the United States.Copyright © 2015 John Wiley & Sons, Inc.

REVIEW QUESTIONS 55 (c) Using just one graph, construct frequency polygons for the two relative frequency distributions. NOTE: When segmenting the horizontal axis, assign the same width to the open-ended interval (65–above) as to any other class interval. (This tactic causes some distortion at the upper end of the histogram, since one class interval is doing the work of several. Nothing is free, including the convenience of open-ended intervals.)