The following are the steps of constructing a frequency distribution: [1]
- Specify the number of class intervals. A class is a group (category) of interest. No totally accepted rule tells us how many intervals are to be used. Between 5 and 15 class intervals are generally recommended. Note that the classes must be both mutually exclusive and all-inclusive*.
- When all intervals are to be the same width, the following
rule may be used to find the required class interval width:
W =
= 
where:
W= class width, L= the largest data, S= the smallest data, K= number of classes
* Mutually exclusive means that classes must be selected such that an item can't fall into two classes and all-inclusive classes are classes that together contain all the data.
Did You Know
A jiffy is an actual scientific measurement.[2]
- In electronics, a jiffy is 1/60 of a second
- In astrophysics and quantum physics a jiffy is the time it takes for light to travel one fermi (the size of a nucleon or about 3 × 10−29 seconds.
Examples
|
7.29 |
7.03 |
7.14 |
6.77 |
6.35 |
7.16 |
6.78 |
6.79 |
7.07 |
7.03 |
|
6.69 |
7.02 |
7.40 |
7.16 |
6.96 |
6.87 |
6.80 |
7.10 |
7.13 |
6.95 |
|
6.98 |
7.56 |
6.75 |
6.87 |
7.11 |
7.08 |
7.24 |
7.34 |
7.47 |
7.31 |
|
7.38 |
7.28 |
6.97 |
6.90 |
6.57 |
6.96 |
6.70 |
6.57 |
6.88 |
6.84 |
|
7.11 |
6.95 |
7.23 |
7.31 |
7.00 |
7.02 |
7.40 |
7.12 |
7.16 |
7.16 |
|
7.30 |
7.17 |
6.96 |
6.78 |
7.30 |
6.99 |
6.94 |
7.29 |
7.05 |
6.84 |
Construct a frequency distribution for these data. Calculate and display the class midpoints, relative frequencies and cumulative frequencies for this frequency distribution.
Solution In Brief
First calculate the size (width) of the class:
We round the class width to 0.20. Each class interval will be exactly 0.20 wide. Starting at or below the smallest number in the range, we increment each interval by 0.20.
