Construction of frequency distribution - SS1 Economics Lesson Note
Frequency distribution is a way to organize and analyze data by grouping it into intervals (or classes) and counting how many observations fall into each interval. The following steps can be followed to construct a frequency distribution:
-
Determine the range of the data: Find the difference between the maximum and minimum values in the data set. This will give you an idea of the spread of the data.
Decide on the number of intervals (or classes): Choose an appropriate number of intervals based on the size of the data set and the range of the data. As a general rule, you should have at least 5-10 intervals, but no more than 20.
Determine the width of the intervals: Divide the range of the data by the number of intervals to determine the width of each interval. Round up or down to create intervals that are easy to work with.
Create the intervals: Create intervals that are non-overlapping and cover the entire range of the data.
Tally the data: Count the number of observations that fall into each interval.
Calculate the frequency: Divide the number of observations in each interval by the total number of observations to calculate the frequency of each interval.
Construct the frequency distribution table: Construct a table that displays the intervals, the frequency, and the cumulative frequency (the sum of the frequencies up to that interval).
Create a histogram: Plot the intervals on the x-axis and the frequency on the y-axis to create a histogram that visually displays the frequency distribution.
Word problems
Suppose a teacher wants to analyze the test scores of her students in a class of 30 students. The scores are as follows:
80, 65, 75, 85, 90, 92, 75, 80, 70, 72, 85, 88, 90, 76, 80, 82, 78, 83, 91, 70, 82, 79, 75, 86, 84, 87, 77, 81, 84, 79.
The teacher wants to create a frequency distribution table for these scores, with intervals of 10 points each.
Solution:
To solve this problem, we first need to determine the intervals or classes. Since the scores range from 65 to 92, we can create intervals of 10 points each, starting from 60 to 100. Thus, our intervals will be:
60-69, 70-79, 80-89, 90-99, 100.
Next, we need to count how many scores fall into each interval. We can use a tally chart to do this:
60-69: |
70-79: |||| |||| ||| (12)
80-89: |||| |||| |||| || (16)
90-99: |||| ||| (7)
100: |
Finally, we can summarize this information in a frequency distribution table:
Interval Frequency
60-69= 1
70-79= 12
80-89= 16
90-99= 7
100= 0
So, the frequency distribution table shows that most students (16) scored in the 80-89 interval, while only one student scored in the 60-69 interval and none scored in the 100 intervals.