Lesson 17 Instruction, 1-5

Pre-Test		Post-Test
Q&A	Statistics and Data Analysis

Showing Orderly Data with Histograms
CA GR5 SDAP 1.2, CA GR6 MR 2.4, CA GR7 AF 1.5, CA GR7 SDAP 1.1

In Bar Graphs, the categories that data came from were related, but not numerical. In Line Graphs, the categories were related by a chronological and numerical order. A histogram is a special kind of Bar Graph where the categories are in numerical order and they are being grouped into intervals. For example, think about a survey that asks for the age of community college students. Instead of asking exact age, the survey groups the ages into intervals that are 10 years wide by having the respondent check a box for their age in one of the following intervals: 6 to 15, 16 to 25 or 26 to 35 or 36 to 45 or 46 to 55 or 56 to 65 or 66 to 75 or 76 to 85. Each interval is 10 years wide, and every person between the ages of 6 and 85 fits in an interval.

Of course, this method is less accurate because once you group the data like this, you can no longer track the exact age, but at least you know how many fell in that range. Once the number of respondents is known for each interval, a modified Bar Graph is drawn. The modifications are that the bars are drawn standing next to each other without gaps, and each is labeled on the horizontal axis at the endpoints.

For example, let us imagine that we poll 20 people at a community college and get the following results for their ages:

#	Age
1	15
2	44
3	32
4	33
5	27
6	22
7	47
8	62
9	25
10	22
11	21
12	43
13	18
14	19
15	21
16	25
17	29
18	31
19	24
20	27

Let us now carefully tally up who belongs to what age interval

Age Interval	Person #
6 – 15	1
16 – 25	6, 9, 10, 11, 13, 14, 15, 16, 19
26 – 35	3, 4, 5, 17, 18, 20
36 – 45	2, 12
46 – 55	7
56 – 65	8
66 – 75
76 – 85

Then simply record the number of people tallied up. The amount is called the frequency.

Age Interval	Frequency
6 – 15	1
16 – 25	9
26 – 35	6
36 – 45	2
46 – 55	1
56 – 65	1
66 – 75	0
76 – 85	0

This frequency data is what is drawn into the modified Bar Chart to make a Histogram:

By examining a Histogram, you can immediately see obvious trends, such as the fact that nearly all the college students in this survey were somewhere between 16 and 36 years old, with one younger and a few more who are no older than 66.

Now let's do Practice Exercise 17-3

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