Constructing Frequency Distribution Table

1. FREQUENCY
DISTRIBUTIONS AND
THEIR GRAPHS

2. 2
LEARNING OBJECTIVES
1. Construct a frequency distribution
that includes classes, frequencies,
midpoints or class marks, relative
frequencies, and cumulative
frequencies.
2. Construct frequency histograms,
frequency polygons, relative
frequency histograms, and ogives.

3. 3
Upper
Class
Limits
FREQUENCY DISTRIBUTIONS
Class Frequency, f
1 – 4 4
5 – 8 5
9 – 12 3
13 – 16 4
17 – 20 2
A frequency distribution is a table that shows
classes or intervals of data with a count of the
number in each class. The frequency f of a class
is the number of data points in the class.
Frequencies
Lower
Class
Limits

4. 4
FREQUENCY DISTRIBUTIONS
Class Frequency, f
1 – 4 4
5 – 8 5
9 – 12 3
13 – 16 4
17 – 20 2
The class width/ class interval size is the distance
between lower (or upper) limits of consecutive classes.
The class interval size (i ) is 4.
5 – 1 = 4
9 – 5 = 4
13 – 9 = 4
17 – 13 = 4
The range is the difference between the
maximum and minimum data entries.

5. 5
CONSTRUCTING A FREQUENCY DISTRIBUTION
Guidelines
1. Decide on the number of classes to include. 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 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 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.

6. 6
CONSTRUCTING A FREQUENCY
DISTRIBUTION
18 20 21 27 29 20
19 30 32 19 34 19
24 29 18 37 38 22
30 39 32 44 33 46
54 49 18 51 21 21
Example:
The following data represents the ages of 30 students in
a statistics class. Construct a frequency distribution
that has five classes.
Continued.
Scores of Students

7. 7
CONSTRUCTING A FREQUENCY
DISTRIBUTION
18 18 18 19 19 19
20 20 21 21 21 22
24 27 29 29 30 30
32 32 33 34 37 38
39 44 46 49 51 54
Array - It is an arrangement of data
according to size or magnitude (ascending
order or descending order.
Continued.
Scores of Students (ascending order)

8. 8
CONSTRUCTING A FREQUENCY DISTRIBUTION
Example continued:
Continued.
1. The number of classes (5) is stated in the problem.
2. The lowest data entry is 18 and highest entry is 54, so
the range is 36. Divide the range by the number of
classes to find the class interval size.
Range – the difference of the lowest from the highest
entry
Class interval size(i) =
36
5
= 7.2 Round up to 8.

9. 9
CONSTRUCTING A FREQUENCY DISTRIBUTION
Example continued:
3. The minimum data entry of 18 may be used for the
lower limit of the first class. To find the lower class
limits of the remaining classes, add the interval size
(8) to each lower limit.
The lower class limits are 18, 26, 34, 42, and 50.
The upper class limits are 25, 33, 41, 49, and 57.
4. Make a tally mark for each data entry in the
appropriate class.
5. The number of tally marks for a class is the frequency
for that class.

10. 10
CONSTRUCTING A FREQUENCY DISTRIBUTION
Example continued:
2
50 – 57
3
42 – 49
4
34 – 41
8
26 – 33
13
18 – 25
Tally Frequency, f
Class
30
f
 
Number of
students
Ages
Check that the
sum equals
the number in
the sample.
Scores of Students