Distribution of Frequency

1. Cumulative Frequency Distribution
Presented By: Mahrukh Shehzadi

2. What is cumulative frequency distribution ?
Cumulative frequency
• The total frequency of all classes less
than the upper class boundary of a given
class is called the cumulative frequency
of that class.
Cumulative frequency distribution
• A table showing the cumulative
frequencies is called a cumulative
frequency distribution.
← Cumulative frequency
distribution
Class boundaries Frequency Cumulative frequency
0-10 5 5
10-20 10 5+10=15
20-30 15 15+15=30
30-40 10 30+10=40

3. Cumulative Frequency Distribution.
• Cumulative frequency distribution is a form of a frequency distribution that represents the sum of
a class and all classes below it.
• The cumulative frequency distribution is extremely helpful when we need to determine the
frequency up to a certain threshold.
• A cumulative frequency table is a simple visual representation of the cumulative frequencies for
each distinct value or category.

4. How To Create A Table?
• Lets take an example:
Class boundaries 5-6 6-7 7-8 8-9 9-10
frequency 1 2 5 9 3
To construct a cumulative frequency distribution:
1) The cumulative frequency of a distinct category is calculated by finding the sum of a category’s
frequency and the total frequencies of all categories below it.
2) Let’s find the cumulative frequencies for a few categories in our example:
Cumulative Frequency (5-6) = 1
Cumulative Frequency (6-7) = 1 + 2 = 3 and so on..

5.  Cumulative Frequency Distribution.
Class boundaries Frequency Cumulative frequency
5-6 1 1
6-7 2 1+2=3
7-8 5 3+5=8
8-9 9 8+9=17
9-10 3 17+3=20

6.  Types Of Cumulative Frequency Distribution.
• There are two types of cumulative frequency distributions.
• Less than cumulative frequency distribution:
 It is obtained by adding successively the frequencies of all the previous classes including the class
against which it is written. The cumulate is started from the lowest to the highest size.
• More than cumulative frequency distribution:
 It is obtained by finding the cumulate total of frequencies starting from the highest to the lowest
class.

8. How To Make An Ogive Or Polygon.
Class limit 4-6 7-9 10-12 13-15
Frequency 2 4 8 3
To make a polygon or ogive.
1. Mark the class boundaries on the x-axis and frequency on y-axis.
2. Plot the points for the given frequency corresponding to the upper class boundaries.
3. Join the points by mean of line segments.
4. Drop the perpendicular from the last point in order to make a closed image.

9. POLYGON OR OGIVE.
Class boundaries Frequency Cumulative
1.5-3.5 0 0
3.5-6.5 2 0+2=2
6.5-9.5 4 2+4=6
9.5-12.5 8 6+8=14
12.5-15.5 3 14+3=17

11. QUESTION:
• Draw a cumulative frequency
graph for the frequency table
below.
Length (x mm) Frequency
11 – 15 2
16 – 20 4
21 – 25 8
25 – 30 14
31 – 35 6
36 – 40 4
41 – 45 2

12. SOLUTION.
• We need to add a class with 0
frequency before the first class
and then find the upper boundary
for each class interval.
Length
(x mm)
Frequency Upper Class
Boundary
Length
(x mm)
Cumulative
Frequency
6 – 10 0 10.5 x ≤ 10.5 0
11 – 15 2 15.5 x ≤ 15.5 2
16 – 20 4 20.5 x ≤ 20.5 6
21 – 25 8 25.5 x ≤ 25.5 14
25 – 30 14 30.5 x ≤ 30.5 28
31 – 35 6 35.5 x ≤ 35.5 34
36 – 40 4 40.5 x ≤ 40.5 38
41 – 45 2 45.5 x ≤ 45.5 40

13. GRAPH
• And then plot the cumulative
frequency against the upper class
boundary of each interval and join
the points with a smooth curve.