Section 2.1, Frequency Distributions and Their Graphs
The main characteristics we will use to describe a data set are its center, its variability, and its
shape. One way to see patterns in data is to make a graph. In this section, we will look at 3 ways
to graphically summarize data: frequency distributions, frequency histograms, and a cumulative
frequency graph.
1 Frequency distribution
Afrequency distribution is a table that shows “classes” or “intervals” of data entries with a count
of the number of entries in each class. The frequency fof a class is the number of data entries in
the class. Each class will have a “lower class limit” and an “upper class limit” which are the lowest
and highest numbers in each class. The “class width” is the distance between the lower limits of
consecutive classes. The range is the difference between the maximum and minimum data entries.
Steps for constructing a frequency distribution from a data set
1. If the number of classes is not given, decide on a number of classes to use. This number should
be between 5 and 20.
2. Find the class width: Determine the range of the data and divide this by the number of classes.
Round up to the next convenient number (if it’s a whole number, also round up to the next
whole number).
3. Find the class limits: You can use the minimum data entry as the lower limit of the first
class. To get the lower limit of the next class, add the class width. Continue until you reach
the last class. Then find the upper limits of each class (since the classes cannot overlap, and
occasionally your data will include decimal numbers, remember that it’s fine for the upper
limits to be decimals).
4. Count the number of data entries for each class, and record the number in the row of the table
for that class. (The book recommends using “tally” marks to count)
Example
Make a frequency distribution for the following data, using 5 classes:
510 719251215768
17 17 22 21 7 7 24 5 6 5
The smallest number is 5, and the largest is 25, so the range is 20. The class width will be 20/5 = 4,
but we need to round up, so we will use 5. Our classes will be 5–9, 10–14, 15–19, 20–24, and 25–29.
Then, counting the number of entries in each class, we get:
Class Frequency
5–9 10
10–14 2
15–19 4
20–24 3
25–29 1
Note that the sum of the frequencies is 20, which is the same as number of data entries that we had.
You can add more information to your frequency distribution table. The “midpoint” (or “class
mark”) of each class can be calculated as:
Midpoint = Lower class limit + Upper class limit
2.
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