Histograms
Histogram is
represented for grouped frequency distribution. In a histogram, we draw bars of
uniform width adjacent to each other. All the class intervals in a histogram are taken along
Xaxis and their respective frequencies on Yaxis.
Marks

Number of students

40 – 50

1

50 – 60

2

60 – 70

5

70 – 80

12

80 – 90

10

90 – 100

20

100 –
110

22

110 –
120

14

120 –
130

6

130 –
140

4

What is a Histogram?
36

25

38

46

55

68

72

55

36

38

67

45

22

48

91

46

52

61

58

55

Marks

Frequency

Marks
Included in Bin

2030

2

25,22

3040

4

36,38,36,38

4050

4

46,45,48,46

5060

5

55,55,52,58,55

6070

3

68,67,61

7080

1

72

8090

0



90100

1

91

When to Use a Histogram?
Difference Between a Histogram and a Bar Graph
How to Draw a Histogram?
Solved Examples on Histogram
Class Interval

Frequency

20 – 30

8

30 – 40

5

40 – 50

6

50 – 60

3

60 – 70

4

70 – 80

5

80 – 90

4

90 – 100

3

Example 3: The following table shows the
heights of 50 students.
Height (in cm) 
Frequency 
150 – 155 
7 
155 – 160 
12 
160 – 165 
18 
165 – 170 
10 
170 – 175 
3 
a. Represent the data using a histogram.
b. Describe the shape of the histogram.
Solution: a. The histogram is shown as follows.
b. The
histogram shows that the heights of most students lie between 160 cm and 165
cm. There are more students in the lowest class than in the highest class.
Example 4: The given histogram shows the number of hours 30
students spend outdoor on a holiday.
a. What is the size of each class interval?
b. How many students spend less than an hour outdoors?
c. In which time interval did the largest number of
students spend time outdoors?
d. How many students spend four or more hours
outdoors?
Solution: a. The class intervals
are 1 – 2, 2 – 3, 3 – 4, …
Thus, class size = 2 – 1 = 1 hour
b. 2 students spend less than an hour outdoors on a
holiday.
c. The largest number of students spend 1 – 2 hours outdoors.
d. 2 students spend four or more hours outdoors.
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