Frequency Distribution
A Frequency Distribution is a grouping of data into mutually
exclusive categories showing the number of observations in each class.
Class limit: The class limits
are the lowest and the highest values that can be included in the class.
Class interval: The class interval is obtained by subtracting
the lower limit of a class from the lower limit of the next class. The class
intervals should be equal. It is denoted here by i
Class Frequency: The number of
observations in each class. It is denoted here by f.
Class Midpoint: A point that
divides a class into two equal parts.
This is the average of the upper and lower class limits.
Construction of
frequency distribution:
Example:
Mr. Rahman is a professor of X University. He wishes prepare to a report showing the
number of hours per week students spend studying. He selects a random sample of 30 students and
determines the number of hours each student studied last week.
15.0, 23.7, 19.7, 15.4, 18.3, 23.0, 14.2, 20.8, 13.5, 20.7, 17.4, 18.6,
12.9, 20.3, 13.7, 21.4, 18.3, 29.8, 17.1, 18.9, 10.3, 26.1, 15.7, 14.0, 17.8,
33.8, 23.2, 12.9, 27.1, 16.6.
Organize the data into a frequency distribution
Step One: First arrange the data in
ascending order. Then we get the data as:
10.3, 12.9, 12.9, 13.5, 13.7, 14, 14.2, 15, 15.4, 15.7, 16.6,17.1,
17.4, 17.8, 18.3, 18.3, 18.6, 18.9,
19.7, 20.3, 20.7, 20.8, 21.4, 23, 23.2, 23.7, 26.1, 27.1, 29.8, 33.8,.
Step Two: Decide on the number of classes using the
formula
Where
k=number of classes
n=number of observations
o
There are 30 observations so n=30.
o
Two raised to the fifth power is 32.
o
Therefore, we should have at least 5 classes, i.e.,
k=5.
Step Three: determine the
class interval or width using the formula
Round up for an interval of 5 hours.
Set the lower limit of the first class at 7.5
hours, giving a total of 6 classes.
Step Four: Set the individual class limits and
Steps Five and Six: Tally and count the number of items in each
class.
Hours studying
|
Tally
|
Frequency, f
|
7.5 up to 12.5
|
I
|
1
|
12.5 up to 17.5
|
IIII IIII II
|
12
|
17.5 up to 22.5
|
IIII IIII
|
10
|
22.5 up to 27.5
|
IIII
|
5
|
27.5 up to 32.5
|
I
|
1
|
32.5 up to 37.5
|
I
|
1
|
No comments:
Post a Comment