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JEE Main Mathematics Statistics Practice Questions

Question 1.

If the variance of the frequency distribution

$x$	$c$	$2 c$	$3 c$	$4 c$	$5 c$	$6 c$
$f$	2	1	1	1	1	1

is 160, then the value of $c \in N$ is

Question 2.

The frequency distribution of the age of students in a class of 40 students is given below.

Age	15	16	17	18	19	20
No of Students	5	8	5	12	$x$	$y$

If the mean deviation about the median is 1.25, then $4 x + 5 y$ is equal to :

Question 3.

The mean and standard deviation of 20 observations are found to be 10 and 2 , respectively. On rechecking, it was found that an observation by mistake was taken 8 instead of 12. The correct standard deviation is

1.94

\sqrt{3.96}

\sqrt{3.86}

1.8

Question 4.

Let $α, β \in R$ . Let the mean and the variance of 6 observations $- 3, 4, 7, - 6, α, β$ be 2 and 23, respectively. The mean deviation about the mean of these 6 observations is :

\frac{16}{3}

\frac{11}{3}

\frac{14}{3}

\frac{13}{3}

Question 5.

Consider 10 observations

x_{1}, x_{2}, \dots, x_{10}

such that

\sum_{i = 1}^{10} (x_{i} - α) = 2

and

\sum_{i = 1}^{10} {(x_{i} - β)}^{2} = 40

, where

α, β

are positive integers. Let the mean and the variance of the observations be

\frac{6}{5}

and

\frac{84}{25}

respectively. Then

\frac{β}{α}

is equal to :

\frac{5}{2}

\frac{3}{2}

Question 6.

Let the median and the mean deviation about the median of 7 observation

170, 125, 230, 190, 210

, a, b be 170 and

\frac{205}{7}

respectively. Then the mean deviation about the mean of these 7 observations is :

Question 7.

Let the mean and the variance of 6 observations $a, b, 68, 44, 48, 60$ be $55$ and $194$ , respectively. If $a > b$ , then $a + 3 b$ is

180

210

190

200

Question 8.

Let M denote the median of the following frequency distribution

Class	0 - 4	4 - 8	8 - 12	12 - 16	16 - 20
Frequency	3	9	10	8	6

Then 20M is equal to :

104

208

416

Question 9.

If the mean and variance of five observations are $\frac{24}{5}$ and $\frac{194}{25}$ respectively and the mean of the first four observations is $\frac{7}{2}$ , then the variance of the first four observations in equal to

\frac{5}{4}

\frac{4}{5}

\frac{105}{4}

\frac{77}{12}

Question 10.

Let

a_{1}, a_{2}, \dots a_{10}

be 10 observations such that

\sum_{k = 1}^{10} a_{k} = 50

and

\sum_{\forall k < j} a_{k} \cdot a_{j} = 1100

. Then the standard deviation of

a_{1}, a_{2}, \dots, a_{10}

is equal to :

\sqrt{115}

\sqrt{5}

Question 1.

The mean and standard deviation of 10 observations are 20 and 8 respectively. Later on, it was observed that one observation was recorded as 50 instead of 40. Then the correct variance is :

Question 2.

Let the mean of 6 observations $1, 2, 4, 5, x$ and $y$ be 5 and their variance be 10 .Then their mean deviation about the mean is equal to :

\frac{10}{3}

\frac{8}{3}

\frac{7}{3}

Question 3.

Let sets A and B have 5 elements each. Let the mean of the elements in sets A and B be 5 and 8 respectively and the variance of the elements in sets A and B be 12 and 20 respectively. A new set C of 10 elements is formed by subtracting 3 from each element of $A$ and adding 2 to each element of $B$ . Then the sum of the mean and variance of the elements of $C$ is ___________.

Question 4.

Let $μ$ be the mean and $σ$ be the standard deviation of the distribution

$x_{i}$	0	1	2	3	4	5
$f_{i}$	$k + 2$	$2 k$	$k^{2} - 1$	$k^{2} - 1$	$k^{2} + 1$	$k - 3$

where $\sum f_{i} = 62$ . If $[x]$ denotes the greatest integer $\leq x$ , then $[μ^{2} + σ^{2}]$ is equal to :

Question 5.

Let the mean and variance of 12 observations be $\frac{9}{2}$ and 4 respectively. Later on, it was observed that two observations were considered as 9 and 10 instead of 7 and 14 respectively. If the correct variance is $\frac{m}{n}$ , where $m$ and $n$ are coprime, then $m + n$ is equal to :

317

316

314

315

Question 6.

The mean and variance of a set of 15 numbers are 12 and 14 respectively. The mean and variance of another set of 15 numbers are 14 and $σ^{2}$ respectively. If the variance of all the 30 numbers in the two sets is 13 , then $σ^{2}$ is equal to :

Question 7.

Let $9 = x_{1} < x_{2} < \dots < x_{7}$ be in an A.P. with common difference d. If the standard deviation of $x_{1}, x_{2} . . ., x_{7}$ is 4 and the mean is $\bar{x}$ , then $\bar{x} + x_{6}$ is equal to :

2 (9 + \frac{8}{\sqrt{7}})

18 (1 + \frac{1}{\sqrt{3}})

Question 8.

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 observations is :

1792

1216

1456

1072

Question 9.

Let the mean and standard deviation of marks of class A of 100 students be respectively 40 and

α (>

0 ), and the mean and standard deviation of marks of class

B

n

students be respectively 55 and 30

- α

. If the mean and variance of the marks of the combined class of

100 + n

studants arerespectively 50 and 350 , then the sum of variances of classes

A

and

B

is :

450

900

650

500

Question 10.

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}, \dots ., a_{100}

is 25 . Then

S

is :

{9}

ϕ

{99}

JEE Main Statistics Practice Questions With Solutions

JEE Main Mathematics Statistics Practice Questions

Question 1.

Question 2.

Question 3.

Question 4.

Question 5.

Question 6.

Question 7.

Question 8.

Question 9.

Question 10.

Question 1.

Question 2.

Question 3.

Question 4.

Question 5.

Question 6.

Question 7.

Question 8.

Question 9.

Question 10.

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