JEE Mathematics - Statistics Chapter Sample Question Paper With Answer Key
Exam Duration: 60 Mins Total Questions : 50
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)
\(k\ \overline{x}+10\)
To determine the intelligence quotient of students, the most suitable measure of the central location, is
- (a)
mean
- (b)
median
- (c)
mode
- (d)
quartiles
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 best measure of dispersion is
- (a)
range
- (b)
standard deviation
- (c)
quartile deviation
- (d)
mean deviation
A sample of 35 observations has the mean 80 and S.D, as 4. A second sample of 65 observations from the same population has mean 70 and S.D.3. The S.D.of the combined sample is
- (a)
5.85
- (b)
5.58
- (c)
34.2
- (d)
NONE OF THESE
The mean and S.D.of the marks of 200 candidates were found to be 40 and 15 respectively. Later, it was discovered that a score 40 was read wrong as 50. The correct mean and S.D.respectively are
- (a)
14.98,39.95
- (b)
39.95,14.98
- (c)
39.95,224.5
- (d)
NONE OF THESE
The mean square deviation of a set of observations x1,x2,x3,......xn about a points C is defined as \(\frac { 1 }{ n } \sum _{ i=1 }^{ n }{ \left( { { x }_{ i }-c }^{ 2 } \right) } \)The mean square deviation about -1 and +1 of a set of observations are 7 and 3 respectively. The standard deviation of this set of observation is
- (a)
\(\sqrt { 2 } \)
- (b)
\(\sqrt { 3 } \)
- (c)
2
- (d)
NONE OF THESE
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
The mean deviation and coefficient of mean deviation about the median from the data of weight (in kg) 54,50,40,42,51,45,47,55,57 is
- (a)
4.5, 0.0900
- (b)
4.78, 0.0956
- (c)
3.8, 0.0056
- (d)
4.96, 0.0946
Find the mean deviation about the mean of the following data.
Size | 1 | 3 | 5 | 7 | 9 | 11 | 13 | 15 |
---|---|---|---|---|---|---|---|---|
Frequency | 3 | 3 | 4 | 14 | 7 | 4 | 3 | 4 |
- (a)
2.95
- (b)
3.24
- (c)
4
- (d)
2
The SD of a variate x is \(\sigma\). The SD of the variate \(ax+b\over c\), where a,b and c are constants is
- (a)
\(({a\over c})\sigma\)
- (b)
\(\begin{vmatrix} \frac { a }{ c } \end{vmatrix}\sigma \)
- (c)
\(({a^2\over C^2})\sigma\)
- (d)
None of these
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
The means of two samples of size 200 and 300 were found to be 25 and 10, respectively. Their standard deviations were 3 and 4, respectively. The variance of the combined sample of size 500 is
- (a)
64
- (b)
65.2
- (c)
67.2
- (d)
642
The sum of squares of deviations taken from mean 50 is 250. The coeficient of variation is
- (a)
10%
- (b)
40%
- (c)
50%
- (d)
None of these
If the mean deviation of numbers 1,1+d,1+2d,...,1+100d from their mean is 255, then d is equal to
- (a)
10.0
- (b)
20.0
- (c)
10.1
- (d)
20.2
Statement I: The variance of first n even natural numbers is \(n^2-1\over4\)
Statement II: The sum of first n natural numbers is \(n(n+1)\over2\) and the sum of squares of first n natural numbers is \(n(n+1)(2n+1)\over6\)
- (a)
Statement I is true, statement II is true; Statement II is the correct explanation for statement I.
- (b)
Statement I is true, Statement II is true; Statement II is not a correct explanation for statement I
- (c)
Statement I is true, Statement II is false
- (d)
Statement I is false, statement II is true
The mena of the numbers a,b,8,5,10 is 6 and the variance is 6.80. Then, which one of the following gives possible values of a and b?
- (a)
a=3, b=4
- (b)
a=0, b=7
- (c)
a=5,b=2
- (d)
a=1,b=6
The mean of a set of numbers is \(\bar { x } \). If each item is decreased by 4, then mean of new observations (set is
- (a)
unaltered
- (b)
raised by 4 units in \(\bar { x } \)
- (c)
reduced by 4 units in \(\bar { x } \)
- (d)
None of these
If x1, x2,x3,....,xn is the set of n observations whose mean is x, then
- (a)
\(\sum _{ i=1 }^{ n }{ ({ x }_{ i }-\bar { x } )\ge 0 } \)
- (b)
\(\sum _{ i=1 }^{ n }{ ({ x }-\bar { x_{ i } } )=0 } \)
- (c)
\(\sum _{ i=1 }^{ n }{ ({ x_{ i } }-\bar { x } )=0 } \)
- (d)
\(\sum { ({ x }_{ i }-\bar { x } )^{ 2 }=0 } \)
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 the data 2, 9, 9, 3, 6, 9, 4 from the mean is
- (a)
2.23
- (b)
2.57
- (c)
3.23
- (d)
3.57
The scores of batsman A in 10 different test matches were 38, 70, 48, 34, 42, 55, 63, 46, 54,44. Find the mean deviation about median.
- (a)
8.6
- (b)
10.61
- (c)
6.8
- (d)
9.61
Find the mean deviation about the mean for the following data.
xi | 2 | 5 | 6 | 8 | 10 | 12 |
fi | 2 | 8 | 10 | 7 | 8 | 5 |
- (a)
3.3
- (b)
6.3
- (c)
2.3
- (d)
5
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
Calculate the mean deviation about the median for the following data.
Class | 16-20 | 21-25 | 26-30 | 31-35 | 36-40 | 41-45 | 46-50 | 51-55 |
Frequency | 5 | 6 | 12 | 14 | 26 | 12 | 16 | 9 |
- (a)
9.35
- (b)
7.35
- (c)
26
- (d)
14.35
The mean of five numbers is 0 and their variance is 2. If three of those numbers are -1, 1 and 2, then the other two numbers are
- (a)
-5 and 3
- (b)
-4 and 2
- (c)
-3 and 1
- (d)
-2 and 0
The mean of 5 observations is 4.4 and their variance is 8.24. If three of the observations are 1, 2 and 6, find the other two observations.
- (a)
4, 9
- (b)
3, 9
- (c)
4, 4
- (d)
9, 9
A set of n values x1, x2, ....,xn has standard deviation \(\sigma \). The standard deviation of n values x1 + k, x2+k, ..., xn + k will be
- (a)
\(\sigma \)
- (b)
\(\sigma \) + k
- (c)
\(\sigma \) - k
- (d)
k\(\sigma \)
The frequency distribution table is given here.
xi | 4 | 8 | 11 | 17 | 20 | 24 | 32 |
fi | 3 | 5 | 9 | 5 | 4 | 3 | 1 |
Find the variance.
- (a)
45.8
- (b)
46.8
- (c)
47.8
- (d)
48.8
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 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
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
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
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 median.
- (a)
2.238
- (b)
4.238
- (c)
3.238
- (d)
5.238
From a frequency distribution consisting of 18 observations, the mean and the standard deviation were found to be 7 and 4 respectively. But on comparison with the original data, it was found that a figure 12 was miscopied as 21 in calculations.
Find the correct mean.
- (a)
9.5
- (b)
8.5
- (c)
6.5
- (d)
7.5
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
Let a, b, c, d, e be the observations with mean m and standard deviation s. The standard deviation of the observations a + k, b + k, c + k, d + k, e + k is
- (a)
s
- (b)
ks
- (c)
s + k
- (d)
\(\frac { s }{ k } \)
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
Coefficient of variation of two distributions are 50% and 60%, and their arithmetic means are 30 and 25 respectively. Difference of their standard deviation is
- (a)
0
- (b)
1
- (c)
1.5
- (d)
2.5
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.
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.
The scores of batsman A in 10 different test matches were 38, 70, 48, 34, 42, 55, 63, 46, 54, 44. Find the standard deviation.
- (a)
10.61
- (b)
8.6
- (c)
9.61
- (d)
6.8
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 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
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
If x and y are two variables such that \(\frac { { \sigma }_{ x } }{ \bar { x } } >\frac { { \sigma }_{ y } }{ \bar { y } } \) then
- (a)
x is more consistent than y
- (b)
y is more consistent than x
- (c)
y is more consistent than x
- (d)
None of these
Following are the marks obtained, out of 100, by two students Ravi and Hashina in 10 tests.
Ravi | Hashina |
25 | 10 |
50 | 70 |
45 | 50 |
30 | 20 |
70 | 95 |
42 | 55 |
36 | 42 |
48 | 60 |
35 | 48 |
60 | 80 |
Who is more intelligent and who is more consistent?
- (a)
Ravi is more consistent and intelligent.
- (b)
Hashina is more consistent and intelligent.
- (c)
Ravi is more consistent and Hashina is more intelligent.
- (d)
Ravi is more intelligent and Hashina is more consistent.
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