"Mean, median, mode and draw cumulative frequency curves (ogives)"
The numerical representation of the ungrouped data called measures of central tendency, namely,
mean, median and mode. we shall extend the study of these three measures, i.e.,
mean, median and mode from ungrouped data to that of grouped data. We shall
also discuss the concept of cumulativ e
frequency, the cumulative frequency distribution and how to draw cumulative
frequency curves, called ogives.
Set-01
1. The
class mark of the class 10 – 25 is: (A) 17 (B) 18 (C) 17.5 (D) 15
2. Find the mean of the following frequency distribution [by assumed mean method]
|
Class
:
|
0
– 6
|
6
– 12
|
12
– 18
|
18
– 24
|
24
– 30
|
|
Frequency
:
|
7
|
5
|
10
|
12
|
6
|
3. Find the mode of the following frequency distribution
|
Class
:
|
0
– 6
|
6
– 12
|
12
– 18
|
18
– 24
|
24
– 30
|
|
Frequency
:
|
7
|
5
|
10
|
12
|
6
|
4. If the mean of the following distribution is 27, find the value of p
|
Class
:
|
0
– 10
|
10
– 20
|
20
– 30
|
30
– 40
|
40
– 50
|
|
Frequency
:
|
8
|
p
|
12
|
13
|
10
|
5. Find mean, and median for the following data :
|
Class
:
|
0
– 10
|
10
– 20
|
20
– 30
|
30
– 40
|
40
– 50
|
|
Frequency
:
|
8
|
16
|
36
|
34
|
6
|
6. Draw ‘less than’ and ‘more than’ ogives for the following distribution:
|
Scores
:
|
20
– 30
|
30
– 40
|
40
– 50
|
50
– 60
|
60
– 70
|
70
– 80
|
|
Frequency
:
|
8
|
10
|
14
|
12
|
4
|
2
|
7. Find the value of f1 from the following data if its mode is 65:
|
Class
|
0
– 20
|
20
– 40
|
40
– 60
|
60
– 80
|
80
– 100
|
100
– 120
|
|
Frequency
|
6
|
8
|
f1
|
12
|
6
|
5
|
Set-02
1. If the „less than‟ type ogive and „more than‟ type ogive intersect each other at (20.5, 15.5), then the median of the given data is : (A) 36.0 (B) 20.5 (C) 15.5 (D) 5.5 [01]
2. Find the sum of lower limit of mediun class and the upper limit of model class : [02]
|
Classes
:
|
10
– 20
|
20
– 30
|
30
– 40
|
40
– 50
|
50
– 60
|
60
– 70
|
|
Frequency
:
|
1
|
3
|
5
|
9
|
7
|
3
|
3. Convert the following data into more than type distribution :[02]
|
Class
:
|
50
– 55
|
55
– 60
|
60
– 65
|
65
– 70
|
70
– 75
|
75
– 80
|
|
Frequency
:
|
2
|
8
|
12
|
24
|
38
|
16
|
4. Draw the less than type ogive for the following data and hence find the median from it.[03]
|
Classes
:
|
50
– 60
|
60
– 70
|
70
– 80
|
80
– 90
|
90
– 100
|
|
Frequency
:
|
6
|
5
|
9
|
12
|
6
|
5. The median of the following frequency distribution is 28.5 and the sum of all the frequencies is 60. Find the values of „p‟ and „q‟ : [03]
|
Classes
:
|
0
– 10
|
10
– 20
|
20
– 30
|
30
– 40
|
40
– 50
|
50
– 60
|
|
Frequency
:
|
5
|
p
|
20
|
15
|
q
|
5
|
6. Calculate the average daily income (in `) of the following data about men working in a company :[05]
|
Daily
income (in `)
|
<
100
|
<
200
|
<
300
|
<
400
|
<
500
|
|
Number
of men
|
12
|
28
|
34
|
41
|
50
|
7. The
distribution below shows the number of wickets taken by bowlers in one-day
cricket matches. Find the mean n umber of wickets by choosing a suitable
method. What does the mean signify? [Hint: Here, the class size varies, and the
x , s are large. Let us still apply the stepdeviation method with a =
200 and h = 20]
|
Number
of wickets
|
20
- 60
|
60
- 100
|
100
- 150
|
150
– 250
|
250
– 350
|
350
- 450
|
|
Number
of bowlers
|
7
|
5
|
16
|
12
|
2
|
3
|
8. Draw a
more than ogive for the following distribution and hence find its median.
|
Class
|
20
– 30
|
30
– 40
|
40
– 50
|
50
– 60
|
60
– 70
|
70
– 80
|
80
– 90
|
|
Frequency
|
25
|
15
|
10
|
6
|
24
|
12
|
8
|
SET-03
1. Relationship among mean, median and mode is :
(A) 3
Median =Mode +2 Mean (B) 3 Mean = Median +
2 Mode
(C) 3
Mode = Mean+2 Median (D) Mode = 3 Mean - 2
Median
2 . Calculate the median for the following distribution :
|
Marks
obtained
|
Number
of students
|
|
Below
10
|
6
|
|
Below
20
|
15
|
|
Below
30
|
29
|
|
Below
40
|
41
|
|
Below
50
|
60
|
|
Below
60
|
70
|
3. Compute the arithmetic mean for the following data :
|
Marks
obtained
|
No.
of students
|
|
Less
than 10
|
14
|
|
Less
than 20
|
22
|
|
Less
than 30
|
37
|
|
Less
than 40
|
58
|
|
Less
than 50
|
67
|
|
Less
than 60
|
75
|
4. Find the missing frequencies f1 and f2 in the following frequency distribution table, if N =100 and median is 32.
|
Class
:
|
0
– 10
|
10
– 20
|
20
– 30
|
30
– 40
|
40
– 50
|
50
– 60
|
Total
|
|
Frequency
|
10
|
f1
|
25
|
30
|
f2
|
10
|
100
|
5. For
the following frequency distribution, draw a cumulative frequency curve of less
than type.
|
Class
:
|
200
– 250
|
250
– 300
|
300
– 350
|
350
– 400
|
400
– 450
|
450
– 500
|
500
– 550
|
550
– 600
|
|
Frequency:
|
30
|
15
|
45
|
20
|
25
|
40
|
10
|
15
|
6. The median class for the following data is
|
Class
|
20
– 40
|
40
– 60
|
60
– 80
|
80
– 100
|
|
Frequency
|
10
|
12
|
20
|
22
|
(A) 20 -
40 (B) 40 - 60 (C) 60 - 80 (D) 80 – 100
7. Write the following frequency distribution as “more than type” and “less than type” cumulative frequency distribution.
|
Class
:
|
0
– 10
|
10
– 20
|
20
– 30
|
30
– 40
|
40
– 50
|
|
Frequency
:
|
5
|
15
|
20
|
23
|
17
|
8. Find
the median for the following table which shows the daily wages drawn by 200
workers in a factory.
|
Daily
wages (in Rs.)
|
Less
than 100
|
Less
than 200
|
Less
than 300
|
Less
than 400
|
Less
than 500
|
|
No.
of workers
|
40
|
82
|
154
|
184
|
200
|
9. The mean of the data in the following table is 50. Find the missing frequencies f1 and f2.
|
Class
:
|
10
– 30
|
30
– 50
|
50
– 70
|
70
– 90
|
90
– 110
|
Total
|
|
Frequency
:
|
90
|
f1
|
30
|
f2
|
40
|
200
|
10. Find the unknown entries a, b, c, d, e and f in the following distribution and hence find their mode.
|
Height
(in cm) :
|
150–155
|
155–160
|
160–165
|
165–170
|
170–175
|
175–180
|
Total
|
|
Frequency
:
|
12
|
b
|
10
|
d
|
e
|
2
|
50
|
|
Cumulative
frequency :
|
a
|
25
|
c
|
43
|
48
|
f
|
|
