## MCQ (Single Correct Answer)

Let $$9=x_{1} ...

In a binomial distribution $$B(n,p)$$, the sum and the product of the mean and the variance are 5 and 6 respectively, then $$6(n+p-q)$$ is equal to...

The mean and variance of 5 observations are 5 and 8 respectively. If 3 observations are 1, 3, 5, then the sum of cubes of the remaining two observatio...

Let the mean and standard deviation of marks of class A of 100 students be respectively 40 and $\alpha(>$
0 ), and the mean and standard deviation of...

Let $S$ be the set of all values of $a_1$ for which the mean deviation about the mean of 100 consecutive positive integers $a_1, a_2, a_3, \ldots ., a...

Three rotten apples are mixed accidently with seven good apples and four apples are drawn one by one without replacement. Let the random variable X de...

The mean and variance of the marks obtained by the students in a test are 10 and 4 respectively. Later, the marks of one of the students is increased ...

Let the six numbers $$\mathrm{a_1,a_2,a_3,a_4,a_5,a_6}$$, be in A.P. and $$\mathrm{a_1+a_3=10}$$. If the mean of these six numbers is $$\frac{19}{2}$$...

If the mean deviation about median for the numbers 3, 5, 7, 2k, 12, 16, 21, 24, arranged in the ascending order, is 6 then the median is

The number of values of a $$\in$$ N such that the variance of 3, 7, 12, a, 43 $$-$$ a is a natural number is :

Let the mean and the variance of 5 observations x1, x2, x3, x4, x5 be $${24 \over 5}$$ and $${194 \over 25}$$ respectively. If the mean and variance o...

The mean and variance of the data 4, 5, 6, 6, 7, 8, x, y, where x ...

Let X be a random variable having binomial distribution B(7, p). If P(X = 3) = 5P(x = 4), then the sum of the mean and the variance of X is :

The mean and standard deviation of 50 observations are 15 and 2 respectively. It was found that one incorrect observation was taken such that the sum ...

The mean of the numbers a, b, 8, 5, 10 is 6 and their variance is 6.8. If M is the mean deviation of the numbers about the mean, then 25 M is equal to...

The mean and variance of 7 observations are 8 and 16 respectively. If two observations are 6 and 8, then the variance of the remaining 5 observations ...

The mean and standard deviation of 20 observations were calculated as 10 and 2.5 respectively. It was found that by mistake one data value was taken a...

Let the mean and variance of the frequency distribution$$\matrix{
{x:} & {{x_1} = 2} & {{x_2} = 6} & {{x_3} = 8} & {{x_4} = 9} \cr...

If the mean and variance of the following data : 6, 10, 7, 13, a, 12, b, 12 are 9 and $${{37} \over 4}$$ respectively, then (a $$-$$ b)2 is equal to :...

The first of the two samples in a group has 100 items with mean 15 and standard deviation 3. If the whole group has 250 items with mean 15.6 and stand...

If the mean and variance of six observations 7, 10, 11, 15, a, b are 10 and $${{20} \over 3}$$, respectively, then the value of | a $$-$$ b | is equal...

The mean of 6 distinct observations is 6.5 and their variance is 10.25. If 4 out of 6 observations are 2, 4, 5 and 7, then the remaining two observati...

Let in a series of 2n observations, half of them are equal to a and remaining half are equal to $$-$$a. Also by adding a constant b in each of these o...

Consider three observations a, b, and c such that b = a + c. If the standard deviation of a + 2, b + 2, c + 2 is d, then which of the following is tru...

If $$\sum\limits_{i = 1}^n {\left( {{x_i} - a} \right)} = n$$ and $$\sum\limits_{i = 1}^n {{{\left( {{x_i} - a} \right)}^2}} = na$$
(n, a > 1) th...

If the mean and the standard deviation of the
data 3, 5, 7, a, b are 5 and 2 respectively, then
a and b are the roots of the equation :

The mean and variance of 7 observations are 8 and 16, respectively. If five observations are 2, 4, 10, 12, 14, then the absolute difference of the rem...

The mean and variance of 8 observations are 10 and 13.5, respectively. If 6 of these observations
are 5, 7, 10, 12, 14, 15, then the absolute differen...

Let xi
(1 $$ \le $$ i $$ \le $$ 10) be ten observations of a
random variable X. If $$\sum\limits_{i = 1}^{10} {\left( {{x_i} - p} \right)} = 3$$ and...

For the frequency distribution :
Variate (x) : x1 x2 x3
.... x15
Frequency (f) : f1
...

Let X = {x
$$ \in $$ N : 1
$$ \le $$ x
$$ \le $$ 17} and
Y = {ax + b: x
$$ \in $$ X and a, b $$ \in $$ R, a > 0}. If mean
and variance of elements ...

Let the observations xi (1 $$ \le $$ i $$ \le $$ 10) satisfy the
equations, $$\sum\limits_{i = 1}^{10} {\left( {{x_1} - 5} \right)} $$ = 10 and $$\sum...

The mean and variance of 20 observations are
found to be 10 and 4, respectively. On
rechecking, it was found that an observation 9
was incorrect and t...

The mean and the standard deviation (s.d.) of
10 observations are 20 and 2 resepectively.
Each of these 10 observations is multiplied by
p and then re...

If the data x1, x2,......., x10 is such that the mean of first four of these is 11, the mean of the remaining six is
16 and the sum of squares of all ...

Let a random variable X have a binomial distribution with mean 8 and variance 4. If $$P\left( {X \le 2} \right) = {k \over {{2^{16}}}}$$, then k
is eq...

If both the mean and the standard deviation of 50 observations x1, x2,..., x50 are equal to 16, then the mean of (x1 – 4)2
, (x2 – 4)2
,....., (x50 – ...

If for some x $$ \in $$ R, the frequency distribution of the marks obtained by 20 students in a test is :
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The mean and the median of the following ten
numbers in increasing order 10, 22, 26, 29, 34, x,
42, 67, 70, y are 42 and 35 respectively, then $${y \o...

If the standard deviation of the numbers
–1, 0, 1, k is $$\sqrt 5$$ where k > 0, then k is equal to

A student scores the following marks in five tests
:
45, 54, 41, 57, 43.
His score is not known for the
sixth test. If the mean score is 48 in the s...

The mean and variance of seven observations are
8 and 16, respectively. If 5 of the observations are
2, 4, 10, 12, 14, then the product of the remaini...

The mean and the variance of five observations are 4 and 5.20, respectively. If three of the observations are
3, 4 and 4 ; then the absolute value of ...

If the sum of the deviations of 50 observations from 30 is 50, then the mean of these observations is :

The outcome of each of 30 items was observed; 10 items gave an outcome $${1 \over 2}$$ – d each, 10 items gave outcome $${1 \over 2}$$ each and the re...

If mean and standard deviation of 5 observations x1, x2, x3, x4, x5 are 10 and 3, respectively, then the variance of 6 observations x1, x2, ….., x5 an...

The mean of five observations is 5 and their variance is 9.20. If three of the given five observations are 1, 3 and 8, then a ratio of other two obser...

A data consists of n observations : x1, x2, . . . . . . ., xn.
If $$\sum\limits_{i = 1}^n {{{\left( {{x_i} ...

5 students of a class have an average height 150 cm and variance 18 cm2. A new student, whose height is 156 cm, joined them. The variance (in cm2) of ...

The mean and the standarddeviation(s.d.) of five observations are9 and 0, respectively. If one of the observations is changed such that the mean of th...

If $$\sum\limits_{i = 1}^9 {\left( {{x_i} - 5} \right)} = 9$$ and
$$\sum\limits_{i = 1}^9 {{{\left( {{x_i} - 5} \right)}^2}} = 45$$, then the standa...

If the mean of the data : 7, 8, 9, 7, 8, 7, $$\lambda $$, 8 is 8, then the variance of this data is :

The mean of set of 30 observations is 75. If each observation is multiplied by a non-zero number $$\lambda $$ and then each of them is decreased by 25...

The sum of 100 observations and the sum of their squares are 400 and 2475,
respectively. Later on, three observations, 3, 4 and 5, were found to be in...

The mean age of 25 teachers in a school is 40 years. A teacher retires at the age of 60 years and a new teacher is appointed in his place. If now the...

The mean of 5 observations is 5 and their variance is 124. If three of the observations
are 1, 2 and 6 ; then the mean deviation from the mean of the ...

If the mean deviation of the numbers 1, 1 + d, ..., 1 +100d from their mean is 255, then a value of d is :

If the standard deviation of the numbers 2, 3, a and 11 is 3.5, then which of the following is true?

The mean of the data set comprising of 16 observations is 16. If one of the observation valued 16 is deleted
and three new observations valued 3, 4 an...

The variance of first 50 even natural numbers is

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 follo...

Let x1, x2,........., xn be n observations, and let $$\overline x $$ be their arithematic mean and $${\sigma ^2}$$ be their variance.
Statement 1 : Va...

If the mean deviation about the median of the numbers a, 2a,........., 50a is 50, then |a| equals

For two data sets, each of size 5, the variances are given to be 4 and 5 and the corresponding
means are given to be 2 and 4, respectively. The varian...

If the mean deviation of number 1, 1 + d, 1 + 2d,........, 1 + 100d from their mean is 255, then the d is
equal to

Statement - 1 : The variance of first n even natural numbers is $${{{n^2} - 1} \over 4}$$
Statement - 2 : The sum of first n natural numbers is $${{n\...

The mean 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?

The average marks of boys in a class is 52 and that of girls is 42. The average marks of boys
and girls combined is 50. The percentage of boys in the ...

Suppose a population A has 100 observations 101, 102,........, 200, and another
population B has 100 observations 151, 152,......., 250. If VA and VB ...

If in a frequently distribution, the mean and median are 21 and 22 respectively, then
its mode is approximately

Let x1, x2,...........,xn be n observations such that
$$\sum {x_i^2} = 400$$ and $$\sum {{x_i}} = 80$$. Then a
possible value of n among the followi...

Consider the following statements:
(a) Mode can be computed from histogram
(b) Median is not independent of change of scale
(c) Variance is indepen...

In a series of 2n observations, half of them equal $$a$$ and remaining half equal $$–a$$. If the
standard deviation of the observations is 2, then $$|...

In an experiment with 15 observations on $$x$$, then following results were available:
$$\sum {{x^2}} = 2830$$, $$\sum x = 170$$
One observation tha...

The median of a set of 9 distinct observations is 20.5. If each of the largest 4 observations of
the set is increased by 2, then the median of the new...

In a class of 100 students there are 70 boys whose average marks in a subject are 75. If the average marks of the complete class is 72, then what is t...

## Numerical

If the variance of the frequency distribution
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The mean and variance of 7 observations are 8 and 16 respectively. If one observation 14 is omitted and a and b are respectively mean and variance of ...

Let $$X=\{11,12,13,....,40,41\}$$ and $$Y=\{61,62,63,....,90,91\}$$ be the two sets of observations. If $$\overline x $$ and $$\overline y $$ are thei...

Let the mean and the variance of 20 observations $$x_{1}, x_{2}, \ldots, x_{20}$$ be 15 and 9 , respectively. For $$\alpha \in \mathbf{R}$$, if the me...

Let $$x_{1}, x_{2}, x_{3}, \ldots, x_{20}$$ be in geometric progression with $$x_{1}=3$$ and the common ratio $$\frac{1}{2}$$. A new data is construct...

The mean and variance of 10 observations were calculated as 15 and 15 respectively by a student who took by mistake 25 instead of 15 for one observati...

The mean and standard deviation of 40 observations are 30 and 5 respectively. It was noticed that two of these observations 12 and 10 were wrongly rec...

Suppose a class has 7 students. The average marks of these students in the mathematics examination is 62, and their variance is 20. A student fails in...

The mean and standard deviation of 15 observations are found to be 8 and 3 respectively. On rechecking it was found that, in the observations, 20 was ...

If the mean deviation about the mean of the numbers 1, 2, 3, .........., n, where n is odd, is $${{5(n + 1)} \over n}$$, then n is equal to __________...

Let X be a random variable with distribution.
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An online exam is attempted by 50 candidates out of which 20 are boys. The average marks obtained by boys is 12 with a variance 2. The variance of mar...

Let n be an odd natural number such that the variance of 1, 2, 3, 4, ......, n is 14. Then n is equal to _____________.

Let the mean and variance of four numbers 3, 7, x and y(x > y) be 5 and 10 respectively. Then the mean of four numbers 3 + 2x, 7 + 2y, x + y and x ...

Consider the following frequency distribution :
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Consider the following frequency distribution :
Class :
0 $$ - $$ 6
6 $$ - $$ 12
12 $$ - $$ 18
18 $$ - $$ 24
24 $$ - $$ 30...

The mean age of 25 teachers in a school is 40 years. A teacher retires at the age of 60 years and a new teacher is appointed in his place. If the mean...

Consider a set of 3n numbers having variance 4. In this set, the mean of first 2n numbers is 6 and the mean of the remaining n numbers is 3. A new set...

Consider the statistics of two sets of observations as follows :
Size
Mean
Variance
Observation I
10
2
2
...

Let X1, X2, ......., X18 be eighteen observations such that $$\sum\limits_{i = 1}^{18} {({X_i} - } \alpha ) = 36$$ and $$\sum\limits_{i = 1}^{18} {({X...

If the variance of 10 natural numbers 1, 1, 1, ....., 1, k is less than 10, then the maximum possible value of k is ________.

Consider the data on x taking the values 0, 2, 4,
8,....., 2n with frequencies nC0
,
nC1
,
nC2
,....,
nCn
respectively. If the mean of this data is $$...

If the variance of the following frequency
distribution :
Class : 10–20 20–30 30–40
Frequency : ...

If the variance of the terms in an increasing A.P., b1
, b2
, b3
,....,b11 is 90, then the common
difference of this A.P. is_______....

If the mean and variance of eight numbers 3, 7, 9, 12, 13, 20, x and y be 10 and 25 respectively,
then x.y is equal to _______.

If the variance of the first n natural numbers is 10 and the variance of the first m even natural
numbers is 16, then m + n is equal to_____.