This document provides instructions for representing grouped data using a histogram, frequency polygon, and ogive. It includes the steps to construct a frequency table from sample data, and then draw the different graphs using the frequency table. The histogram, frequency polygon, and ogive are drawn with the class intervals on the x-axis and frequency/cumulative frequency on the y-axis.

1. Represent grouped data
by using
histogram,
frequency polygon and
ogive

2. To construct / complete a frequency table
30 58 53 67 56 51 61 56 54 75
71 31 63 39 41 50 52 46 72 50
42 60 34 78 45 76 43 66 48 63
86 80 64 66 53 70 52 59 65 61
Tally Marks Frequency Complete the
class interval
30 - 39 4 Click to show
40 - 49 6
Tallying
50 - 59 12 Click to show
60 - 69 10
Frequency
70 - 79 6 Click to show
80 - 89 2

3. To Draw A Histogram Marks Freq
Mid
point
Scale : x-axis : 2 cm to 10 marks
Frequency 30-39 4 34.5
y-axis : 2 cm to 2 students
40-49 6 44.5
12 50-59 12 54.5
60-69 10 64.5
10 70-79 6 74.5
80-89 2 84.5
8
6
4
2
30-39 40-49 50-59 60-69 70-79 80-89
Marks
2 cm
x-axis is marked with class interval

4. To Draw A Frequency Polygon Marks Freq
Mid
point
Scale : x-axis : 2 cm to 10 marks
Frequency 20-29 0 24.5
y-axis : 2 cm to 2 students
30-39 4 34.5
12 40-49 6 44.5
50-59 12 54.5
10 60-69 10 64.5
70-79 6 74.5
8
80-89 2 84.5
6 90-99 0 94.5
4
Ends with
frequency = 0
2
24.5 34.5 44.5 54.5 64.5 74.5 84.5 94.5
Starts with Marks
frequency = 0
x-axis is marked with midpoint 2 cm

5. Frequency polygon Scale : x-axis : 2 cm to 10 marks
y-axis : 2 cm to 2 students
Frequency
Frequency polygon can
12
be drawn from a
10 histogram
8
6
4
2
34.5 44.5 54.5 64.5
2 cm Marks
x-axis is marked with midpoint

6. To Draw An Ogive
Marks Frequency Upper Boundary Cumulative Frequency
20-29 0 (29 + 30) / 2 = 29.5 0
30-39 4 (39 + 40) / 2 = 39.5 0+4=4
40-49 6 (49 + 50) / 2 = 49.5 4 + 6 = 10
50-59 12 (59 + 60) / 2 = 59.5 10 + 12 = 22
60-69 10 (69 + 70) / 2 = 69.5 22 + 10 = 32
70-79 6 (79 + 80) / 2 = 79.5 32 + 6 = 38
80-89 2 (89 + 90) / 2 = 89.5 38 + 2 = 40
Complete the
Upper Boundary
Click to show
Students must determine the last value for
Complete the Cumulative last cumulative frequency equal to the
Frequency number of the frequency given in the
Click to show
questions.

7. Cumulative To Draw An Ogive
Frequency
Scale :
40 y-axis is marked x-axis :
with 2 cm to 10 marks
35
Cumulative Frequency y-axis :
30 2 cm to 5 students
25
20
15
x-axis is marked
10 with
Upper Boundary
5
0 Marks
29.5 39.5 49.5 59.5 69.5 79.5 89.5
2 cm