Mathematics - Statistics
Exam Duration: 45 Mins Total Questions : 30
The mean of first n natural numbers, is
- (a)
\(\frac { n }{ 2 } \)
- (b)
\(\frac { n\left( n+1 \right) }{ 2 } \)
- (c)
\(\frac { \left( n+1 \right) }{ 2 } \)
- (d)
\(\frac { \left( n+1 \right) }{ 2 } \)
The mean of squares of first n natural numbers, is
- (a)
\(\frac { \left( n+1 \right) }{ 2 } \)
- (b)
\(\frac { n }{ 2 } \)
- (c)
\(\frac { 2n+1 }{ 6 } \)
- (d)
\(\frac { \left( n+1 \right) \left( 2n+1 \right) }{ 6 } \)
The mean of the series a,a+d,a+2d,......, a+(n-1)d is
- (a)
a+nd
- (b)
\(\frac { a+nd }{ 2 } \)
- (c)
\(a+\frac { (n-1)d }{ 2 } \)
- (d)
\(a+\frac { (n+1)d }{ 2 } \)
The measure of the central tendency which is not affected by the extreme values :
- (a)
mean
- (b)
median
- (c)
geometric mean
- (d)
harmonic mean
The mode of the data given below 41,42,45,46,44,45,48,50,45 is
- (a)
45
- (b)
44
- (c)
42
- (d)
41
The first quartile \(\left( { Q }_{ 1 } \right) \) and third quartile \(\left( { Q }_{ 3 } \right) \) for the series 8,9,11,12,13,17,20 are
- (a)
9,17
- (b)
11,13
- (c)
9,13
- (d)
NONE OF THESE
The standard deviation of first n natural numbers is
- (a)
\(\frac { n(n+1)(2n+1) }{ 6 } \)
- (b)
\(\frac { { n }^{ 2 }-1 }{ 12 } \)
- (c)
\(\sqrt { \frac { { n }^{ 2 }-1 }{ 12 } } \)
- (d)
NONE OF THESE
Sum of the absolute deviations of the data \({ x }_{ 1 }<{ x }_{ 2 }<{ x }_{ 3 }<....{ x }_{ 101 },{ x }_{ 102 }<...<{ x }_{ 201 }\) is the least when taken from
- (a)
\({ x }_{ 1 }\)
- (b)
\({ x }_{ 201 }\)
- (c)
\({ x }_{ 101 }\)
- (d)
\(\frac { { x }_{ 1 }+{ x }_{ 2 }+{ x }_{ 3 }+......{ x }_{ 201 } }{ 201 } \)
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
The range of the following set of observations 2, 3, 5, 9, 8, 7, 6, 5, 7, 4, 3 is
- (a)
11
- (b)
7
- (c)
5.5
- (d)
6
The mean of the first (n+1) natural numbers is
- (a)
\(\frac { (n+2) }{ 2 } \)
- (b)
\(\frac { (n+1)(n+2) }{ 2 } \)
- (c)
\({ \left[ \frac { n(n+1) }{ 2 } \right] }^{ 2 }\)
- (d)
\(\frac { (n+1) }{ 2 } \)
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%
A batsman in his 16th innings makes a score of 70 runs, and thereby increases his average by 2 runs. If he had never been 'not out', then his average after 16th innings is
- (a)
36
- (b)
38
- (c)
40
- (d)
42
The mean deviation of items x, x + y, x + 2y, ... , x + 2ny from mean is
- (a)
\(\frac { n(n+1)y }{ 2n+1 } \)
- (b)
\(\frac { (n+1)y }{ 2n+1 } \)
- (c)
\(\frac { ny }{ 2n+1 } \)
- (d)
\(\frac { (2n+1)y }{ n(n+1) } \)
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:
Class | 0-10 | 10-20 | 120-30 | 30-40 | 40-50 | 50-60 |
Frequency | 6 | 7 | 15 | 16 | 4 | 2 |
- (a)
10.16
- (b)
11.12
- (c)
12.16
- (d)
9.16
The frequency distribution table is given here.
xi | 10 | 15 | 18 | 20 | 25 |
fi | 3 | 2 | 5 | 8 | 2 |
Find the standard deviation.
- (a)
4.12
- (b)
5.12
- (c)
6.12
- (d)
7.12
The standard deviation of a distribution is 30 and each item is raised by 3, then new S.D. is
- (a)
32
- (b)
28
- (c)
27
- (d)
None of these
Standard deviation of the first 2n + 1 natural numbers is equal to
- (a)
\(\sqrt { \frac { n(n+1) }{ 2 } } \)
- (b)
\(\sqrt { \frac { n(n+1)(2n+1) }{ 3 } } \)
- (c)
\(\sqrt { \frac { n(n+1) }{ 3 } } \)
- (d)
\(\sqrt { \frac { n(n-1) }{ 2 } } \)
The standard deviation of the numbers 31, 32, 33, ......, 46, 47 is
- (a)
\(\sqrt { \frac { 17 }{ 12 } } \)
- (b)
\(\sqrt { \frac { { 47 }^{ 2 }-1 }{ 12 } } \)
- (c)
\(2\sqrt { 6 } \)
- (d)
\(4\sqrt { 3 } \)
In a survey of 950 families in a village, the following distribution of number of children was obtained.
Number of children | 0-2 | 2-4 | 4-6 | 6-8 | 8-10 | 10-12 |
Number of families | 272 | 328 | 205 | 120 | 15 | 10 |
Find the mean.
- (a)
3.545
- (b)
3.543
- (c)
3.443
- (d)
3.343
Following are the marks obtained by 9 students in a mathematics test: 50, 69, 20, 33, 53, 39, 40, 65, 59 Mean deviation from the median is
- (a)
9
- (b)
10.5
- (c)
12.67
- (d)
14.76
Let x1,x2,.....,xn be n observations and \(\bar { x } \) be their arithmetic mean. The formula for the standard deviation is given by
- (a)
\(\sum { { (x-\bar { x } ) }^{ 2 } } \)
- (b)
\(\frac { \sum { { \left( { x }_{ i }-\bar { x } \right) }^{ 2 } } }{ n } \)
- (c)
\(\sqrt { \frac { \sum { { ({ x }_{ i }-\bar { x } ) }^{ 2 } } }{ n } } \)
- (d)
\(\sqrt { \frac { { \sum { x } }_{ i }^{ 2 } }{ n } +{ \bar { x } }^{ 2 } } \)
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 standard deviation of the two samples of variates taken together.
- (a)
9.34
- (b)
4.34
- (c)
4.54
- (d)
9.54
If for a distribution \(\\ \sum { (x-5) } \) = 3, \(\sum { { (x-5) }^{ 2 } } \) = 43 and the total number of items is 18. Find the mean.
- (a)
5.15
- (b)
5.17
- (c)
5.13
- (d)
None of these
The mean and variance of n values of a variable x are 0 and \({ \sigma }^{ 2 }\),respectively. If the variable y = x2, then mean of y is
- (a)
\(\sigma \)
- (b)
\({ \sigma }^{ 2 }\)
- (c)
1
- (d)
\(\sigma /2\)
The variance of the numbers 2, 3, 11 and x is \(\frac { 49 }{ 4 } \). Find the value of x.
- (a)
6,\(\frac { 14 }{ 3 } \)
- (b)
\(6,\frac { 14 }{ 5 } \)
- (c)
\(6,\frac { 16 }{ 3 } \)
- (d)
\(4,\frac { 13 }{ 5 } \)
Coefficient of variation of two distributions are 60% and 75%, and their standard deviations are 18 and 15 respectively. Find their arithmetic means respectively.
- (a)
30, 30
- (b)
30,20
- (c)
20, 30
- (d)
20, 20
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
The mean and standard deviation of a set of n1 observations are \(\\ \\ \\ \\ { \bar { x } }_{ 1 }\) and s1, respectively while the mean and standard deviation of another set of n2 observations are \(\\ \\ \\ \\ { \bar { x } }_{ 2 }\) and s2, respectively. Then the standard deviation of the. combined set of (n1 + n2) observations is given by
- (a)
\(\sqrt { \frac { { n }_{ 1 }{ \left( { s }_{ 1 } \right) }^{ 2 }+{ n }_{ 2 }{ ({ s }_{ 2 }) }^{ 2 } }{ { n }_{ 1 }+{ n }_{ 2 } } +\frac { { n }_{ 1 }{ n }_{ 2 }{ \left( { \bar { x } }_{ 1 }+{ \bar { x } }_{ 2 } \right) }^{ 2 } }{ { \left( { n }_{ 1 }+{ n }_{ 2 } \right) }^{ 2 } } } \)
- (b)
\(\sqrt { \frac { { n }_{ 1 }{ ({ s }_{ 1 }) }^{ 2 }+{ n }_{ 2 }{ \left( { s }_{ 2 } \right) }^{ 2 } }{ { n }_{ 1 }-{ n }_{ 2 } } +\frac { { n }_{ 1 }{ n }_{ 2 }{ \left( { \bar { x } }_{ 1 }-{ \bar { x } }_{ 2 } \right) }^{ 2 } }{ { \left( { n }_{ 1 }+{ n }_{ 2 } \right) }^{ 2 } } } \)
- (c)
\(\sqrt { \frac { { n }_{ 1 }{ ({ s }_{ 1 }) }^{ 2 }-{ n }_{ 2 }{ ({ s }_{ 2 }) }^{ 2 } }{ { n }_{ 1 }+{ n }_{ 2 } } +\frac { { { n }_{ 1 }{ n }_{ 2 } }\left( { \bar { x } }_{ 1 }+{ \bar { x } }_{ 2 } \right) ^{ 2 } }{ { ({ n }_{ 1 }+{ n }_{ 2 }) }^{ 2 } } } \)
- (d)
\(\sqrt { \frac { { n }_{ 1 }{ \left( { s }_{ 1 } \right) }^{ 2 }+{ n }_{ 2 }\left( { s }_{ 2 } \right) ^{ 2 } }{ { n }_{ 1 }+{ n }_{ 2 } } +\frac { { n }_{ 1 }{ n }_{ 2 }{ \left( { \bar { x } }_{ 1 }-{ \bar { x } }_{ 2 } \right) }^{ 2 } }{ { ({ n }_{ 1 }+{ n }_{ 2 }) }^{ 2 } } } \)