Probability and Statistics
Chapter 2
Frequency Distributions and Their Graphs
Section 2.1
Constructing a Frequency Distribution from a Data Set
1.) Decide on the number of classes to include in the frequency distribution. The number of
classes should be between 5 and 20; otherwise, it may be difficult to detect any patterns.
2.) Find the class width as follows. Determine the range of the data, divide the range by the
number of classes, and round up to the next convenient number.
3.) Find the class limits. You can use the minimum data entry as the lower limit of the first
class. To find the remaining lower limits, add the class width to the lower limit of the
preceding class. Then find the upper limit of the first class. Remember that classes
cannot overlap. Find the remaining upper class limits.
4.) Make a tally mark for each data entry in the row of the appropriate class.
5.) Count the tally marks to find the total frequency f for each class.
Example: Constructing a Frequency Distribution from a Data Set
The data set lists the prices (in dollars) of 30 portable global positioning system (GPS) navigtors.
Construct a frequency distribution that has seven classes.
128
100
180
150
200
90
340
105
85
270
200
65
230
150
150
120
130
80
230
200
110
126
170
132
140
112
90
340
170
190
1.) Number of Classes: 7 It is stated in the problem
2.) The minimum data entry is 65 and the maximum data entry is 340, so the range is
340 – 65 = 275. Divide the range by the number of classes and round up to find the class
width.
275
≈ 39.29
7
3.) The nimimum data entry is a convenient lower limit for the first class. To find the lower
limits of the remaining six classes, add the class width of 40 to the lower limit of each
previous class. So, the lower limits of the other classes are
65 + 40 = 105, 105 + 40 = 145, and so on. The upper limit of the first class is 104,
which is one less than the lower limit of the second class. The upper limits of the other
classes are 104 + 40 = 144, 144 + 40 = 184, and so on. Flip and see on the other side.
𝑐𝑙𝑎𝑠𝑠 𝑤𝑖𝑑𝑡ℎ =
Lower Limit
65
105
145
185
225
265
305
Upper Limit
104
144
184
224
264
304
344
4.) Make a tally mark for each data entry in the appropriate class. For instance, the data
entry 128 is in the 105 – 144 class, so make a tally mark in that class. Continue until you
have made a tally mark for each of the 30 data entries.
5.) The number of tally marks for a class is the frequency of that class.
The first class, 65 – 104, has six tally marks. So, the frequency of this class is 6. Notice
that the sum of the frequencies is 30, which is the number of entries in the data set.
Class
65 – 104
105 – 144
145 – 184
185 – 224
225 – 264
265 – 304
305 - 344
Tally
lllll l
lllll llll
lllll l
llll
ll
l
ll
Frequency
6
9
6
4
2
1
2
∑ 𝑓 = 30
In Your Notebooks
Construct a frequency distribution table using the ages of the 50 most powerful women.
1.)
2.)
3.)
4.)
5.)
State the number of classes.
Find the minimum and maximum data entries and the class width.
Find the class limits.
Tally the data entries.
Write the frequency f of each class.
Construct a frequency distribution table for the data set using the indicated number of classes.
Political Blog Reading Times
Number of classes: 5
Data set: Times (in minutes) spent reading a political blog in a day
7
30
39
39
7
16
13
35
15
9
12
25
15
8
8
22
6
0
5
2
29
18
0
2
11