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Graphical Representation & Measures of Central Tendency
Regina Vivek
Facilitator in L’ecole Chempaka
1. Draw histograms to represent the following data:
CI
20-30 30-40 40-50 50-60 60-70
f
3
5
12
7
4
Height
No. of
boys
121130
12
131140
16
141150
30
151160
20
161170
14
171180
1
2. Find the mean of the following numbers: 25, 40, 29, 37, 39, 26, 28.
Now, if each number is increased by 5, then calculate the new
mean.
[32, 37]
3. The mean of 11 observations is 65. If the mean of first six
observations is 63 and that of last six observations is 66; find the
sixth observation.
[59]
4. Two groups of 30 and 50 items have average score 120 and 80
respectively. When a group of 40 items is added to these two
groups, the combined average score of 120 items is 90. Find the
average score of the new group of 40 items.
[80]
5. Calculate the mean for the following distributions:
Wt (kg)
33 38 41 46 51
No. of stu.
4
7
8
2
6
6. Find the mean of the following distribution by short-cut method:
Marks
20-30 30-40 40-50 50-60 60-70 70-80
No. of Students
10
6
8
12
5
9
7. Calculate the mean by step deviation method:
CI
100-120 120-140 140-160 160-180 180-200
f
10
20
30
15
5
8. The mean of the following distribution is 52 and the frequency of
class interval 30 – 40 is ‘f’. Find ‘f’.
CI
10-20 20-30 30-40 40-50 50-60 60-70 70-80
f
5
3
f
7
2
6
13
9. The mean of 1,7,5,3,4 and 4 is ‘m’. The numbers 3, 2, 4, 2, 3, 3 and
‘p’ have mean (m – 1) and median ‘q’. Find ‘p’ and ‘q’.
10. The monthly income of a group of 320 employees in a company is
given below:
Monthly 6000- 7000- 8000- 9000- 10000- 11000- 12000income
7000 8000 9000 1000 11000 12000 13000
No. of
20
45
65
95
60
30
5
Emp.
Draw an ogive taking 2 cm = Rs. 1000 on one axis and 2 cm = 50
employees on other axis. From the graph determine:
i)
The median wage.
ii)
No. of employees whose income is below Rs. 8500
iii)
If the salary of a senior employee is above Rs. 11500, find
the number of senior employees.
iv)
The upper quartile.
11. The result of an examination are tabulated below:
Marks less 10 20 30 40 50 60 70 80 90 100
than
No. of
8 20 40 75 125 160 188 192 197 200
candidates
Taking 2 cm = 10 marks on one axes, 2 cm = 20 candidates on the
other axis, draw the ogive for the above and from it determine:
i)
The number of candidates who failed, if the pass marks is
35.
ii)
The number of candidates who obtained Grade A, if the
lowest mark for Grade A is 75.
iii)
From the graph, estimate median and the interquartile
range.
12. A Mathematics aptitude test of 50 students was recorded as
follows:
Marks
50-60
60-70
70-80
80-90
90-100
No. of Stu.
4
8
14
19
5
Using a graph paper, draw a histogram for the above data, locate
the mode and state the modal class.