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CHAPTER-15
STATISTICS
SECTION – A
TYPE - I
1.
Calculate the mean deviation from the mean for the following data:
(i)
4, 7, 8, 9, 10, 12, 13, 17
(ii)
(iii)
38, 70, 48, 40, 42, 55, 63, 46, 54, 44
13, 17, 16, 14, 11, 13, 10, 16, 11, 18, 12,
17
2.
3.
Calculate the mean deviation about the median of the following observations:
(i)
38, 70, 48, 34, 42, 55, 63, 46, 54, 44
(iii)
3011, 2780, 3020, 2354, 3541, 4150, 5000
34, 66, 30, 38, 44, 50, 40, 60, 42, 51
Calculate the mean deviation of the following income groups of five and seven members from their
medians:
I
Income in Rs.
4000
4200
4400
4600
4800
4.
(ii)
II
Income in Rs.
300
4000
420
4400
4600
4800
5800
The length (in cm) of 10 rods in a shop are given below:
40.0, 52.3, 55.2, 72.9, 52.8, 79.0, 32.5, 15.2, 27.9, 30.2,
(i)
Find mean deviation from median
(ii)
Find mean deviation from the mean also.
TYPE - II
1.
Calculate the mean deviation from the median of the following frequency distribution:
Heights in inches
No. Of students
2.
58
15
59
20
60
32
61
35
62
35
63
22
64
20
65
10
66
8
The number of telephone calls received at an exchange in 245 successive one-minute intervals are
shown in the following frequency distribution:
Number of calls 0
1
2
3
Frequency
14
21
25
43
Compute the mean deviation about median.
4
51
5
40
6
39
7
12
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CHAPTER-15
3.
STATISTICS
Calculate the mean deviation about the medina of the following frequency distribution:
(i)
xi
fi
xi
fi
4.
5
2
7
4
9
6
15 21
3 5
11
8
27 30
6 7
13
10
15
12
17
8
(ii)
35
8
Find the mean deviation from the mean for the following data:
(i)
xi
fi
(ii)
xi
fi
5
8
5
7
7
6
9
2
10
4
10
2
12
2
15 20
6 3
13
6
25
5
TYPE - III
1.
Compute the mean deviation from the median of the following distribution:
2.
Class
0-10 10-20 20-30 30-40 40-50
Frequency
5
10
20
5
10
Find the mean deviation from the mean for the following data:
(i)
C
f
(ii)
Classes
Frequency
(iii)
0-100
4
Classes
Frequency
100-200
8
95-105
9
0-10
6
200-300
9
105-115
13
10-20
8
300-400
10
115-125
16
20-30
14
400-500
7
125-135
26
30-40
16
40-50
4
500-600
5
600-700
4
135-145
30
145-155
12
700-800
3
50-60
2
3.
Find the mean deviation from the mean and from median of the following distribution:
4.
Marks
0-10 10-20 20-30 30-40 40-50
No. Of students 5
8
15
16
6
Calculate mean deviation about median age for the age distribution of 100 persons given below:
Age:
Number of persons
5.
16-20
5
21-25
6
26-30
12
31-35
14
36-40
26
41-45
12
46-50
16
51-55
9
Calculate the mean deviation about the mean for the following frequency distribution:
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CHAPTER-15
Class interval:
Frequency
6.
STATISTICS
0-4
4
4-8
6
8-12
8
12-16
5
16-20
2
Calculate mean deviation from the median of the following data:
Class interval:
Frequency
0-6
4
6-12
5
12-18
3
18-24
6
24-30
2
SECTION – B
TYPE - I
1.
Find the mean, variance and standard deviation for the following data:
(i)
2, 4, 5, 6, 8, 17
(ii)
227, 235, 255, 269, 292, 299, 312, 321, 333, 348
2.
The variance of 20 observations is 5. If each observations is multiplied by 2, find the variance of the
resulting observations.
3.
The variance of 15 observations is 4. If each observation is increased by 9, find the variance of the
resulting observations.
4.
The mean of 5 observations is 4.4 and their variance is 8.24. If three of the observations are1, 2 and
6, find the other two observations.
5.
The mean and standard deviation of 6 observations are 8 and 4 respectively. If each observation is
multiplied by3, find the new mean and new standard deviation of the resulting observations.
6.
The mean and variance of 8 observations are 9 and 25 respectively. If six of the observations are 6, 7,
10, 12, 12 and 13, find the remaining two observations.
7.
The mean and standard deviation of 100 observations were calculated as 40 and 5.1 respectively by a
student who took by mistake 50 instead of 40 for one observation. What are the correct mean and
standard deviation?
8.
The mean and standard deviation of 20 observations are found to be 10 and 2 respectively. On
rechecking it was found that an observation 8 was incorrect. Calculate the correct mean and standard
deviation in each of the following cases:
(i)
If wrong item is omitted
(ii)
If it is replaced by 12.
TYPE - II
1.
Find the standard deviation for the following distribution:
2.
x:
4.5
14.5
24.5
34.5
44.5
54.5
64.5
f:
1
5
12
22
17
9
4
Table below shows the frequency f with which ‘x’ alpha particles were radiated from a diskette:
x:
0
1
2
3
4
5
6
7
8
9
10
11
12
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CHAPTER-15
STATISTICS
f:
51 203 383 525 532
Calculate the mean and variance.
3.
4.
408
273
139
43
27
10
4
2
Find the mean, and standard deviation for the following data:
(i)
Year render:
No. Of persons (cumulative):
10
15
(ii)
Marks:
Frequency:
6
8
2
1
3
6
4
6
5
8
20
32
7
2
8
2
30
51
9
3
40
78
50
97
11
2
12
1
10
0
60
109
13
0
14
0
15
0
16
1
Find the standard deviation for the following data:
(i)
x:
f:
3
7
8
10
(ii)
x:
f:
2
4
3
9
13
15
4
16
18
10
5
14
23
6
6
11
7
6
TYPE - III
1.
Calculate the standard deviation for the following data:
2.
Class:
0-30 30-60 60-90 90-120 120-150 150-180 180-210
Frequency: 9
17
43
82
81
44
24
A student obtained the mean and standard deviation of 100 observation as 40 and 5.1 respectively. It
was later found that one observation was wrongly copied as 50, the correct figure being 40. Find the
correct mean and S.D.
3.
Calculate the mean, median and standard deviation of the following distribution:
4.
Class-interval 31-35
36-40
41-45
46-50
51-55
Frequency
2
3
8
12
16
Find the mean and variance of frequency distribution given below
5.
xi:
1 x  3
3 x 5
5 x7
7  x  10
fi:
6
4
5
1
The weight of coffee in 70 jars is shown in the following table:
56-60
5
61-65
2
Weight (in grams): 200-201 201-202 202-203 203-204 204-205
Frequency
13
27
18
10
1
Determine the variance and standard deviation of the above distribution.
66-70
3
205-206
1
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CHAPTER-15
STATISTICS
SECTION – C
1.
Two plants A and B of a factory show the following about the number of workers and the wages paid
to them
Plant A
Plant B
No. Of workers
5000
6000
Average monthly wages
Rs. 2500
Rs. 2500
Variance of distribution of wages
81
100
In which plant A or B is there greater variability in individual wages?
2.
The means and standard deviations of heights and weights of 50 students of a class are as follows:
Weights
Heights
Mean
63.2 kg
63.2 inch
Standard deviation
5.6 kg
11.5 inch
Which shows more variability, heights or weights?
3.
Coefficient of variation of two distribution are 60% and 70% and their standard deviation are 21 and
16 respectively. What are their arithmetic means?
4.
Calculate coefficient of variation from the following data:
Income 1000-1700
(in Rs.)
No. Of
12
families:
5.
1700-2400
2400-3100
310-3800
3800-4500
4500-5200
18
20
25
35
10
The following are some particulars of the distribution of weights of boys and girls in a class:
Boys
Girls
Number
100
50
Mean weight
60 kg
45 kg
Variance
9
4
Which of the distributions is more variable?
6.
7.
From the data given below state which group is more variable G1 or G2 ?
Marks
10-20
20-30
30-40
40-50
50-60
60-70
70-80
Group G1
Group G2
9
10
17
20
32
30
33
25
42
43
10
15
9
7
Find the coefficient of variation for the following data:
Size (in cms): 10-15
No. Of items: 2
8.
15-20
8
20-25
20
25-30
35
30-35
20
35-40
15
From the prices of shares X and Y given below: find out which is more stable in value:
X:
Y:
35
108
54
109
52
105
53
105
56
106
58
107
52
104
50
103
51
104
49
101
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CHAPTER-15
STATISTICS
Answers (Section – A)
TYPE - I
1. (i)
3
3.
240
(ii)
2.33
(iii)
8.4
4. (i)
16.4
2. (i)
8.6
(ii)
(ii)
16.44
(ii)
5.1
8.7
(iii)
34
4. (i)
3.39
(ii)
3.
9.44, 9.56
TYPE - II
1
1.493
6.32
2.
1.49
3. (i)
2.88
(ii)
11.288
TYPE - III
1.
9
2. (i)
157.92
5.
0.99
6.
7.8
(iii)
10.24
Answers (Section – B)
TYPE - I
1. (i)
7, 23.33, 4.83 (ii)
289.10, 1539.77, 39.24
2.
20
4.
9, 4
5.
18, 12
4, 8
7.
Mean = 39.9, S.D. = 5
2.
X  3.88,  2  3.64
(ii)
X  5.975 , S.D. = 2.85
6.
3.
4
TYPE - II
1.
13.26
3. (i)
X  29.95 years, S.D. = 15.5 years
4. (i)
6.12
(ii)
1.38
TYPE - III
1.
X  118.7,   42.51
2.
X  39.9,   5
3.
X  50,   7.62 , Median =
51.66
4.
Mean = 5.5, Variance = 4.26
5.
Variance = 1.16 gm, S.D. = 1.08 gm
3.
35, 22.85
Answers (Section – C)
1.
Plant B
2.
Heights
5.
Boys
7.
21.86
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Senior Faculty : G D Goenka, Ramjas Public School, KIIT World School St - 6
CHAPTER-15
STATISTICS
MATHS CLASSES by PRAVEEN GUPTA(9811257273,9136487798) www.uniquefoundations.com
Senior Faculty : G D Goenka, Ramjas Public School, KIIT World School St - 7