Statistics Practice Questions - DPP for JEE

 Page 1


PART-I (Single Correct MCQs)
1. Consider any set of observations x
1
, x
2
, x
3
, ...., x
101
; it being given that x
1
< x
2
 < x
3
 < ... < x
100
 < x
101
 ; then the mean deviation of this set of
observations about a point k is minimum when k
equals
(a) x
1
(b) x
51
(c)
(d) x
50
2. Let r be the range and be the S.D. of a set of
observations x
1
,x
2
, ....x
n
, then
(a)
(b)
Page 2


PART-I (Single Correct MCQs)
1. Consider any set of observations x
1
, x
2
, x
3
, ...., x
101
; it being given that x
1
< x
2
 < x
3
 < ... < x
100
 < x
101
 ; then the mean deviation of this set of
observations about a point k is minimum when k
equals
(a) x
1
(b) x
51
(c)
(d) x
50
2. Let r be the range and be the S.D. of a set of
observations x
1
,x
2
, ....x
n
, then
(a)
(b)
(c)
(d) None of these
3. For (2n + 1) observations x
1
, –x
1
, x
2
, –x
2
, .........x
n
, –x
n
 and  0 where x’s
are all distinct. Let S.D. and M.D. denote the standard deviation and
median respectively.Then which of the following is always
true? (a) S.D < M.D.
(b) S.D.> M.D.
(c) S.D. = M.D.
(d) Nothing can be said in general about the relationship of S.D. and M.D.
4. Consider the first 10 positive integers. If we multiply each number by
(– 1) and then add 1 to each number, the variance of the numbers so
obtained is
(a) 8.25
(b) 6.5
(c) 3.87
(d) 2.87
5. Coefficient of variation of two distributions are 50 and 60 and their
arithmetic means are 30 and 25, respectively. Then, difference of their
standard deviations is
(a) 0
(b) 1
(c) 1.5
(d) 2.5
6. 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 of 40 was
wrongly read 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
Page 3


PART-I (Single Correct MCQs)
1. Consider any set of observations x
1
, x
2
, x
3
, ...., x
101
; it being given that x
1
< x
2
 < x
3
 < ... < x
100
 < x
101
 ; then the mean deviation of this set of
observations about a point k is minimum when k
equals
(a) x
1
(b) x
51
(c)
(d) x
50
2. Let r be the range and be the S.D. of a set of
observations x
1
,x
2
, ....x
n
, then
(a)
(b)
(c)
(d) None of these
3. For (2n + 1) observations x
1
, –x
1
, x
2
, –x
2
, .........x
n
, –x
n
 and  0 where x’s
are all distinct. Let S.D. and M.D. denote the standard deviation and
median respectively.Then which of the following is always
true? (a) S.D < M.D.
(b) S.D.> M.D.
(c) S.D. = M.D.
(d) Nothing can be said in general about the relationship of S.D. and M.D.
4. Consider the first 10 positive integers. If we multiply each number by
(– 1) and then add 1 to each number, the variance of the numbers so
obtained is
(a) 8.25
(b) 6.5
(c) 3.87
(d) 2.87
5. Coefficient of variation of two distributions are 50 and 60 and their
arithmetic means are 30 and 25, respectively. Then, difference of their
standard deviations is
(a) 0
(b) 1
(c) 1.5
(d) 2.5
6. 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 of 40 was
wrongly read 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
7. The standard deviation of a variate x is s. The standard deviation of the
variable ; a, b, c are constants, is
(a)
(b)
(c)
(d) None
8. The variance of 20 observations is 5. If each observation is multiplied
by 2, then the new variance of the resulting observation is
(a) 2
3
 × 5
(b) 2
2
 × 5
(c) 2 × 5
(d) 2
4
 × 5
9. The mean deviation from the mean of the A.P. 
a, a + d, a + 2d, ........ a, a + 2nd is
(a) n (n + 1) d
(b)
(c)
(d)
10. The mean and SD of 63 children on an arithmetic test are respectively
27.6 and 7.1. To them are added a new group of 26 who had less
training and whose mean is 19.2 and SD 6.2.  The values of the
combined group differ from the original as to (i) the mean and (ii) the
SD is
Page 4


PART-I (Single Correct MCQs)
1. Consider any set of observations x
1
, x
2
, x
3
, ...., x
101
; it being given that x
1
< x
2
 < x
3
 < ... < x
100
 < x
101
 ; then the mean deviation of this set of
observations about a point k is minimum when k
equals
(a) x
1
(b) x
51
(c)
(d) x
50
2. Let r be the range and be the S.D. of a set of
observations x
1
,x
2
, ....x
n
, then
(a)
(b)
(c)
(d) None of these
3. For (2n + 1) observations x
1
, –x
1
, x
2
, –x
2
, .........x
n
, –x
n
 and  0 where x’s
are all distinct. Let S.D. and M.D. denote the standard deviation and
median respectively.Then which of the following is always
true? (a) S.D < M.D.
(b) S.D.> M.D.
(c) S.D. = M.D.
(d) Nothing can be said in general about the relationship of S.D. and M.D.
4. Consider the first 10 positive integers. If we multiply each number by
(– 1) and then add 1 to each number, the variance of the numbers so
obtained is
(a) 8.25
(b) 6.5
(c) 3.87
(d) 2.87
5. Coefficient of variation of two distributions are 50 and 60 and their
arithmetic means are 30 and 25, respectively. Then, difference of their
standard deviations is
(a) 0
(b) 1
(c) 1.5
(d) 2.5
6. 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 of 40 was
wrongly read 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
7. The standard deviation of a variate x is s. The standard deviation of the
variable ; a, b, c are constants, is
(a)
(b)
(c)
(d) None
8. The variance of 20 observations is 5. If each observation is multiplied
by 2, then the new variance of the resulting observation is
(a) 2
3
 × 5
(b) 2
2
 × 5
(c) 2 × 5
(d) 2
4
 × 5
9. The mean deviation from the mean of the A.P. 
a, a + d, a + 2d, ........ a, a + 2nd is
(a) n (n + 1) d
(b)
(c)
(d)
10. The mean and SD of 63 children on an arithmetic test are respectively
27.6 and 7.1. To them are added a new group of 26 who had less
training and whose mean is 19.2 and SD 6.2.  The values of the
combined group differ from the original as to (i) the mean and (ii) the
SD is
(a) 25.1, 7.8
(b) 2.3, 0.8
(c) 1.5, 0.9
(d) None of these
11. The standard deviations of two sets containing 10 and 20 members are
2 and 3 respectively measured from their common mean 5. The SD for
the whole set of 30 members is
(a)
(b)
(c)
(d)
12. The marks of some students were listed out of 75. The SD of marks was
found to be 9. Subsequently the marks were raised to a maximum of
100 and variance of new marks was calculated. The new variance is
(a) 144
(b) 122
(c) 81
(d) None of these
13. If the variable takes values  with frequencies proportional
to  respectively, the variance is
(a)
(b)
(c)
(d) None of these
14. The standard deviation of  observations  is 2. If 
Page 5


PART-I (Single Correct MCQs)
1. Consider any set of observations x
1
, x
2
, x
3
, ...., x
101
; it being given that x
1
< x
2
 < x
3
 < ... < x
100
 < x
101
 ; then the mean deviation of this set of
observations about a point k is minimum when k
equals
(a) x
1
(b) x
51
(c)
(d) x
50
2. Let r be the range and be the S.D. of a set of
observations x
1
,x
2
, ....x
n
, then
(a)
(b)
(c)
(d) None of these
3. For (2n + 1) observations x
1
, –x
1
, x
2
, –x
2
, .........x
n
, –x
n
 and  0 where x’s
are all distinct. Let S.D. and M.D. denote the standard deviation and
median respectively.Then which of the following is always
true? (a) S.D < M.D.
(b) S.D.> M.D.
(c) S.D. = M.D.
(d) Nothing can be said in general about the relationship of S.D. and M.D.
4. Consider the first 10 positive integers. If we multiply each number by
(– 1) and then add 1 to each number, the variance of the numbers so
obtained is
(a) 8.25
(b) 6.5
(c) 3.87
(d) 2.87
5. Coefficient of variation of two distributions are 50 and 60 and their
arithmetic means are 30 and 25, respectively. Then, difference of their
standard deviations is
(a) 0
(b) 1
(c) 1.5
(d) 2.5
6. 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 of 40 was
wrongly read 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
7. The standard deviation of a variate x is s. The standard deviation of the
variable ; a, b, c are constants, is
(a)
(b)
(c)
(d) None
8. The variance of 20 observations is 5. If each observation is multiplied
by 2, then the new variance of the resulting observation is
(a) 2
3
 × 5
(b) 2
2
 × 5
(c) 2 × 5
(d) 2
4
 × 5
9. The mean deviation from the mean of the A.P. 
a, a + d, a + 2d, ........ a, a + 2nd is
(a) n (n + 1) d
(b)
(c)
(d)
10. The mean and SD of 63 children on an arithmetic test are respectively
27.6 and 7.1. To them are added a new group of 26 who had less
training and whose mean is 19.2 and SD 6.2.  The values of the
combined group differ from the original as to (i) the mean and (ii) the
SD is
(a) 25.1, 7.8
(b) 2.3, 0.8
(c) 1.5, 0.9
(d) None of these
11. The standard deviations of two sets containing 10 and 20 members are
2 and 3 respectively measured from their common mean 5. The SD for
the whole set of 30 members is
(a)
(b)
(c)
(d)
12. The marks of some students were listed out of 75. The SD of marks was
found to be 9. Subsequently the marks were raised to a maximum of
100 and variance of new marks was calculated. The new variance is
(a) 144
(b) 122
(c) 81
(d) None of these
13. If the variable takes values  with frequencies proportional
to  respectively, the variance is
(a)
(b)
(c)
(d) None of these
14. The standard deviation of  observations  is 2. If 
 and  then  is
(a) 10 or 20
(b) 5 or 10
(c) 5 or 20
(d) 5 or 15
15. The coefficient of variation from the given data
is :
(a) 50
(b) 51.9
(c) 48
(d) 51.8
16. All the students of a class performed poorly in Mathematics. The
teacher decided to give grace marks of 10 to each 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
17. Let , .......... be n observations such that = 400 and 
= 80. Then the possible value of n among the following
is (a) 15
(b) 18
(c) 9
(d) 12
18. If  and  then the standard
deviation of the 9 items  is
(a) 9