IISER Mathematics - Statistics
Exam Duration: 45 Mins Total Questions : 30
The one which is the measure of the central tendency, is
- (a)
mode
- (b)
range
- (c)
mean deviation
- (d)
standard deviation
The mean of variate x is \(\overline{x}\). Then mean of the variate \(x+10\over k\), is
- (a)
\(\overline{x}\over k\)
- (b)
\(\overline{x}+10\over k\)
- (c)
\({\overline{x} \over k} +10\)
- (d)
\(k\ \overline{x}+10\)
The geometric mean of 2,22,23,........2n is
- (a)
\({ 2 }^{ n/2 }\)
- (b)
\({ 2 }^{ n/2+1 }\)
- (c)
\(2\frac { n+1 }{ 2 } \)
- (d)
\({ 2 }^{ 2n }\)
Mean deviation of the series a, a+d, a+2d, ......a+2nd from its mean is
- (a)
\(\frac { (n+1)d }{ (2n+1) } \)
- (b)
\(\frac { nd }{ 2n+1 } \)
- (c)
\(\frac { n(n+1)d }{ (2n+1) } \)
- (d)
\(\frac { (2n+1)d }{ n(n+1) } \)
If S.D.of a variate x is \(\sigma \), then S.D.of \(\frac { ax+b }{ c } \),where a,b,c are constants is
- (a)
\(\frac { c }{ a } \sigma \)
- (b)
\(\frac { { c }^{ 2 } }{ { a }^{ 2 } } \sigma \)
- (c)
\(\frac { b }{ c } \sigma \)
- (d)
\(\frac { a }{ c } \sigma \)
In a data distribution
- (a)
\(S.D.\ge M.D.\)
- (b)
\(S.D.
- (c)
\(S.D.\le M.D.\)
- (d)
\(S.D.=M.D.\)
The variance of the data 3,4,5,8 is
- (a)
4.5
- (b)
3.5
- (c)
5.5
- (d)
6.5
Karl pearson's coefficient of skewness of a distribution is 0.32.It standard deviation is 6.5 and mean is 29.6.Then mode and median of the distribution are
- (a)
27.52,28.91
- (b)
27,28
- (c)
26,27
- (d)
28,29
If the standard deviation of y1,y2,...yn is 3.5, then the standard deviation of -2y1-3,-2y2-3,...,-2yn-3 is
- (a)
-7
- (b)
9
- (c)
7
- (d)
2.45
Which of the following data is correct about the standard deviation?
- (a)
standard deviation can be calculated as positive or negative square root of squared deviation
- (b)
Standard deviation is calculated as positive square root of arithmetic mean of squared deviation only
- (c)
standard deviation is independent of change of scales
- (d)
None o the above
Which of the following is a correct statement?
- (a)
Standard deviation is depend on change of origin.
- (b)
Standard deviation is depend on change of scales
- (c)
Median is independent of change of origin
- (d)
Mean is independent of change of scales
If the mean and standard deviation of the marks of 200 candidates of IIT entrance test were found to be 40 and 15, respectively. Later, it was wrongly read as 50. Then, the correct mean and standard deviation are
- (a)
39.95,14.98
- (b)
40.2,14.29
- (c)
30.9,15.9
- (d)
29.32,13.29
Find the mean deviation about the median for the following data.
Xi | 3 | 6 | 9 | 12 | 13 | 15 | 21 | 22 |
fi | 3 | 4 | 5 | 2 | 4 | 5 | 4 | 3 |
- (a)
5.97
- (b)
4.97
- (c)
6.27
- (d)
5.21
Find the mean deviation about the mean for the following data
Marks obtained | Number of students |
---|---|
10-20 20-30 30-40 40-50 50-60 60-70 70-80 |
2 |
- (a)
20
- (b)
25
- (c)
21
- (d)
10
All the students of a class performed poorly in Mathematics. The teacher decided to give grace marks of 10 to eah of the students. Which of the following statistical measures will not change even after the grace marks were given?
- (a)
Mean
- (b)
Median
- (c)
Mode
- (d)
Variance
Suppose population A has 100 observations 101,102,...,200 and another population B has 100 observations 151,152,....,250. If VA and VB represent the variances of the two populations respectively, then \(V_A\over V_B\) is
- (a)
9/4
- (b)
4/9
- (c)
2/3
- (d)
1
If the mean of the distribution
Variate | 6 | 7 | 1.9 | 9 | 10 |
Frequency | 1 | 2 | k | 3 | 4 |
is 3.6. The value of k =
- (a)
30
- (b)
12
- (c)
10
- (d)
11
Mean marks scored by the students of a class is 53. The mean marks of the girls is 55 and the mean marks of the boys is 50. What is the percentage of girls in the class?
- (a)
60%
- (b)
40%
- (c)
50%
- (d)
45%
The arithmetic mean of 7 consecutive integers starting with a is m. Then the arithmetic mean of 11 consecutive integers starting with a + 2 is
- (a)
2a
- (b)
2m
- (c)
a+4
- (d)
m+4
Find the mean deviation about the mean for the following data:
xi | 1 | 4 | 9 | 12 | 13 | 14 | 21 | 22 |
fi | 3 | 4 | 5 | 2 | 4 | 5 | 4 | 3 |
- (a)
5.33
- (b)
4.33
- (c)
6.33
- (d)
8
Calculate the mean deviation from the mean of the following data:
Marks | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 | 60-70 |
Number of students | 4 | 6 | 1 | 20 | 10 | 6 | 4 |
- (a)
12.33
- (b)
11.33
- (c)
20
- (d)
13
Answer the following questions: Find the mean of first 10 multiples of 3.
- (a)
15.5
- (b)
17.5
- (c)
16.5
- (d)
18.5
The frequency distribution table is given here.
Class | 30-40 | 40-50 | 50-60 | 60-70 | 70-80 | 80-90 | 90-100 |
Frequency | 3 | 7 | 12 | 15 | 8 | 3 | 2 |
Find the variance.
- (a)
205
- (b)
203
- (c)
201
- (d)
204
The frequency distribution table is given here.
Classes | Frequency |
---|---|
1-10 | 11 |
11-20 | 29 |
21-30 | 18 |
31-40 | 4 |
41-50 | 5 |
51-60 | 3 |
Find the variance.
- (a)
163.53
- (b)
164.25
- (c)
162.21
- (d)
161.14
Mean deviation for n observations x1,x2, ....., xn from their mean \(\bar { x } \) is given by
- (a)
\(\sum _{ i=1 }^{ n }{ ({ x }_{ i }-\bar { x } ) } \)
- (b)
\(\frac { 1 }{ n } \sum _{ i=1 }^{ n }{ |{ x }_{ i }-\bar { x } | } \)
- (c)
\(\sum _{ i=1 }^{ n }{ { ({ x }_{ i }-\bar { x } ) }^{ 2 } } \)
- (d)
\(\frac { 1 }{ n } \sum _{ i=1 }^{ n }{ { ({ x }_{ i }-\bar { x } ) }^{ 2 } } \)
Statement-I: The variance of first n natural numbers is \(\frac { { n }^{ 2 }-1 }{ 12 } \)
Statement-II: The sum of first n natural numbers is \(\frac { n(n+1) }{ 2 } \) and the sum of squares of first n natural numbers is \(\frac { n(n+1)(2n+1) }{ 6 } \)
- (a)
If both Statement-I and Statement-II are true and Statement-II is the correct explanation of Statement -1.
- (b)
If both Statement -I and Statement-II are true but Statement-II is not the correct explanation of Statement -1.
- (c)
If Statement-I is true but Statement-II is false
- (d)
If Statement-I is false and Statement-II is true.
A sample of 25 variates has the mean 40 and standard deviation 5 and a second sample of 35 variates has the mean 45 and standard deviation 2.
Find the mean of the two sample of variates taken together.
- (a)
43.917
- (b)
49.917
- (c)
42.917
- (d)
44.917
Two plants A and B of a factory show following results about the number of workers and the wages paid to them.
A | 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?
- (a)
B
- (b)
A
- (c)
A = B
- (d)
None of these
Coefficient of variation of two distributions are 60 and 70, and their standard deviations are 21 and 16, respectively. What are their arithmetic means?
- (a)
35,22.85
- (b)
35, 27.85
- (c)
37,22.85
- (d)
37,27.85
Find the C.V. of the following data:
Size (in m) | 10-15 | 15-20 | 20-25 | 25-30 | 30-35 | 35-40 |
No.of items | 2 | 8 | 20 | 35 | 20 | 15 |
- (a)
20.24
- (b)
21.89
- (c)
23.10
- (d)
19.20