Visualizing Variability : A Histogram Exercise

Here is another data set. We want to analyze the selling prices of 33 Hendricks Hill homes (from a 1993 assessor's market study, in thousands of dollars). The list is sorted.

Selling prices of 33 Hendricks Hill area homes, 1993
82.5
115.0
131.0
160.0
185.0
200.0
235.0
89.0
118.9
132.0
162.0
186.5
200.0
265.5
90.0
123.0
137.5
169.0
186.9
208.0
279.5
91.0
123.0
139.0
170.0
187.0
210.0
 –
112.3
130.0
139.9
172.5
199.5
230.0
 –

To make a histogram of this data, you will need to group the numbers into reasonable classes. We want at least five classes; ten is a good number. Look at the range of these prices-- from 82.5 to 279.5. What is the range of the prices?
Dividing the approximate range by 10 gives ten classes of 20 thousand dollars.

The frequency table below is started with tally marks. The first three classes already have tally marks written in. Four tally marks go in the 80-99 class, since four homes (82.5, 89.0, 90.0 and 91.0) fall in the $80,000 to $99,999 interval.

#15 Tally the count in each class. Some people make a horizontally oriented histogram just using equally spaced tally marks.
Price class Tally Frequency
80 - 99 4
100-119 3
120-139 8
140-159
160-179
180-199
200-219
220-239
240-259
260-279
The finished histogram of the Hendricks Hill home selling price data. The class width is 20. There are 10 classes. Classes must be shown even if they are empty, to avoid distorting the information.
#16 What facts about the housing market in the Hendricks Hill area does the histogram suggest to you?
The effect of number of classes and class width
With fewer classes the overall shape of the histogram is clearer, but you lose detail. With too many classes the frequency of each would be 0 or 1! Too much detail. Five classes is the usual minimum.

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