Mathematics - Statistics
Exam Duration: 45 Mins Total Questions : 30
The median of a given data distribution can be determined graphically by
- (a)
frequncy polygon
- (b)
pie-chart
- (c)
histogram
- (d)
ogive
The mean marks of 100 students were found to be 30. Later on it was discovered that a score of 43 was wrongly read as 53. Then the corrected mean is
- (a)
30.9
- (b)
29.9
- (c)
30.1
- (d)
29.1
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)
\({ 2 }^{ 2n }\)
The coefficients of variations for two series are 60% and 80% and their S.Ds. are 20 and 16 respectively. Then there respective means are
- (a)
33.3,20
- (b)
33,20.3
- (c)
34,20
- (d)
34.3,20.3
If g1 and g2 are the geometric means of two series of n1 and n2 items. Then, the GM of the series obtained on combining is
- (a)
\({ [(g_{ 1 })^{ n_{ 1 } }(g_{ 2 })^{ n_{ 2 } }] }^{ \frac { 1 }{ n_{ 1 }+n_{ 2 } } }\)
- (b)
\((g_1g_2)^{n_1\over{n_1+n_2}}\)
- (c)
\((g_1g_2)^{n_1\over{n_1+n_2}}\)
- (d)
\((g_1g_2)^{n_1n_2\over{n_1+n_2}}\)
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
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
If mean of 3, 4, x, 7, 10 is 6 then the value of x is
- (a)
4
- (b)
5
- (c)
6
- (d)
7
The mean of the given data is 30.
Class | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 |
Frequency | 8 | 10 | f1 | 15 | f2 |
If total data is 70, then missing numbers are
- (a)
14, 23
- (b)
25, 21
- (c)
24, 13
- (d)
40, 31
Find the mean deviation about the mean for the following data:
Marks obtained | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 | 60-70 |
Number of students | 8 | 6 | 12 | 5 | 2 | 7 |
- (a)
13.6
- (b)
14.6
- (c)
16.6
- (d)
12.6
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
The mean of five observations is 4 and their variance is 5.2. If three of them are 1, 2, 6, then other two are
- (a)
2, 9
- (b)
4, 7
- (c)
5, 6
- (d)
2, 10
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.
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
If the standard deviation of 3, 8, 6, 10, 12, 9, 11, 10, 12, 7 is 2.71. Then the standard deviation of 30, 80, 60, 100, 120, 90, 110, 110, 120, 70 is
- (a)
2.71
- (b)
27.1
- (c)
(2.71)\(\sqrt { 10 }\)
- (d)
(2.71)\(\sqrt { 2 }\)
The variance of 20 observations is 5. If each observation is multiplied by 2, find the new variance of the resulting observations.
- (a)
80
- (b)
20
- (c)
10
- (d)
50
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 mean.
- (a)
62
- (b)
64
- (c)
65
- (d)
63
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.
Find the correct mean.
- (a)
38.9
- (b)
37.9
- (c)
39.9
- (d)
36.9
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. Find the correct standard deviation.
- (a)
4
- (b)
6
- (c)
3
- (d)
5
The standard deviation of the data 6, 5, 9, 13, 12, 8, 10 is
- (a)
\(\sqrt { \frac { 52 }{ 7 } } \)
- (b)
\(\frac { 52 }{ 7 } \)
- (c)
\(\sqrt { 6 } \)
- (d)
6
The mean of 100 observations is 50 and their standard deviation is 5. The sum of all squares of all the observations is
- (a)
50000
- (b)
250000
- (c)
252500
- (d)
255000
Standard deviation for first 10 natural numbers is
- (a)
5.5
- (b)
3.87
- (c)
2.97
- (d)
2.87
The following information relates to a sample of size 60; \(\sum { { x }^{ 2 } } \) = 18000, \(\sum { x } \) = 960. The variance of the data is
- (a)
6.63
- (b)
16
- (c)
22
- (d)
44
The standard deviation of some temperature data in °C is 5. If the data were converted into °F, the variance would be
- (a)
81
- (b)
57
- (c)
36
- (d)
25
If n is a natural number, then
Statement-I: The mean of the squares of first n natural numbers is \(\frac { (n+1)(2n+1) }{ 6 } \)
Statement-II: \(\sum { n } =\frac { n(n+1) }{ 2 } \)
- (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.
Consider the following data
xi | 6 | 10 | 14 | 18 | 24 | 28 | 30 |
fi | 2 | 4 | 7 | 12 | 8 | 4 | 3 |
Statement-I: The mean of the data is 19.
Statement-II: The variance of the data is 43.4.
- (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.
Statement-I: If u is the mean of a distribution, then \(\sum { { f }_{ i }(y_{ i }-\mu ) } \) is equal to 0.
Statement-II: The mean of the square of first n natural numbers is \(\frac { 1 }{ 6 } n(2n+1)\)
- (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.
Life of bulbs produced by two factories A and B are given below:
Length of life (in hours) | Factory A (Number of bulbs) | Factory B (Number of bulbs) |
---|---|---|
550-650 | 10 | 8 |
650-750 | 22 | 60 |
750-850 | 52 | 24 |
850-950 | 20 | 16 |
950-1050 | 16 | 12 |
120 | 120 |
The bulbs of which factory are more consistent from the point of view of length of life?
- (a)
Factory A
- (b)
Factory B
- (c)
Both are equally consistent
- (d)
None of these
Which of the following statements is/are true?
Statement-I: Mean and standard deviation of 100 observations were found to be 40 and 10, respectively. If at the time of calculation two observations were wrongly taken as 30 and 70 in place of 3 and 27 respectively, then the correct standard deviation is 10.24.
Statement-II: While calculating the mean and variance of 10 readings, a student wrongly used the reading 52 for the correct reading 25. He obtained the mean and variance as 45 and 16 respectively. The correct mean and the variance is 50 and 43.81.
- (a)
Only Statement-I
- (b)
Only Statement-II
- (c)
Both Statement-I and Statement-II
- (d)
Neither Statement-I nor Statement-II