LFM Stats And Pure

jee-main 2017 Q78 View

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 age of the teachers in this school now is 39 years, then the age (in years) of the newly appointed teacher is:
(1) 25
(2) 30
(3) 35
(4) 40

jee-main 2017 Q84 View

If $\sum _ { i = 1 } ^ { 9 } ( x _ { i } - 5 ) = 9$ and $\sum _ { i = 1 } ^ { 9 } ( x _ { i } - 5 ) ^ { 2 } = 45$, then the standard deviation of the 9 items $x _ { 1 } , x _ { 2 } , \ldots , x _ { 9 }$ is:
(1) 9
(2) 4
(3) 2
(4) 3

jee-main 2018 Q73 View

The mean of a set of 30 observation is 75. If each observations is multiplied by non-zero number $\lambda$ and then each of them is decreased by 25, their mean remains the same. Then, $\lambda$ is equal to :
(1) $\frac { 4 } { 3 }$
(2) $\frac { 1 } { 3 }$
(3) $\frac { 10 } { 3 }$
(4) $\frac { 2 } { 3 }$

jee-main 2018 Q74 View

The mean and the standard deviation (S. D.) of five observations are 9 and 0 , respectively. If one of the observation is increased such that the mean of the new set of five observations becomes 10 , then their S. D. is
(1) 0
(2) 2
(3) 4
(4) 1

jee-main 2018 Q74 View

The mean of a set of 30 observations is 75 . If each other observation is multiplied by a nonzero number $\lambda$ and then each of them is decreased by 25 , their mean remains the same. The $\lambda$ is equal to
(1) $\frac { 10 } { 3 }$
(2) $\frac { 4 } { 3 }$
(3) $\frac { 1 } { 3 }$
(4) $\frac { 2 } { 3 }$

jee-main 2018 Q75 View

If $\sum _ { i = 1 } ^ { 9 } \left( x _ { i } - 5 \right) = 9$ and $\sum _ { i = 1 } ^ { 9 } \left( x _ { i } - 5 \right) ^ { 2 } = 45$, then the standard deviation of the 9 items $x _ { 1 } , x _ { 2 } , \ldots , x _ { 9 }$ is
(1) 3
(2) 9
(3) 4
(4) 2

jee-main 2019 Q73 View

If the standard deviation of the numbers $- 1,0,1 , k$ is $\sqrt { 5 }$ where $k > 0$, then $k$ is equal to
(1) $\sqrt { 6 }$
(2) $4 \sqrt { \frac { 5 } { 3 } }$
(3) $2 \sqrt { \frac { 10 } { 3 } }$
(4) $2 \sqrt { 6 }$

jee-main 2019 Q74 View

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 the difference of the other two observations, is :
(1) 3
(2) 5
(3) 7
(4) 1

jee-main 2019 Q74 View

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 six tests, then the standard deviation of the marks in six tests is:
(1) $\frac { 10 } { 3 }$
(2) $\frac { 100 } { 3 }$
(3) $\frac { 10 } { \sqrt { 3 } }$
(4) $\frac { 100 } { \sqrt { 3 } }$

jee-main 2019 Q75 View

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 observations is
(1) $10 : 3$
(2) $4 : 9$
(3) $6 : 7$
(4) $5 : 8$

jee-main 2019 Q75 View

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 $\frac { y } { x }$ is equal to:
(1) $\frac { 9 } { 4 }$
(2) $\frac { 7 } { 3 }$
(3) $\frac { 7 } { 2 }$
(4) $\frac { 8 } { 3 }$

jee-main 2019 Q76 View

A data consists of $n$ observations: $x_1, x_2, \ldots, x_n$. If $\sum_{i=1}^{n}(x_i + 1)^2 = 9n$ and $\sum_{i=1}^{n}(x_i - 1)^2 = 5n$, then the standard deviation of this data is
(1) 5
(2) $\sqrt{7}$
(3) $\sqrt{5}$
(4) 2

jee-main 2020 Q58 View

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 the correct observation was 11, then the correct variance is
(1) 3.99
(2) 4.01
(3) 4.02
(4) 3.98

jee-main 2020 Q58 View

Let $X = \{x \in N : 1 \leq x \leq 17\}$ and $Y = \{ax + b : x \in X$ and $a, b \in R, a > 0\}$. If mean and variance of elements of $Y$ are 17 and 216 respectively then $a + b$ is equal to
(1) 7
(2) $-7$
(3) $-27$
(4) 9

jee-main 2020 Q59 View

Let the observation $x _ { i } ( 1 \leq i \leq 10 )$ satisfy the equations $\sum _ { i = 1 } ^ { 10 } \left( x _ { i } - 5 \right) = 10 , \sum _ { i = 1 } ^ { 10 } \left( x _ { i } - 5 \right) ^ { 2 } = 40$. If $\mu$ and $\lambda$ are the mean and the variance of the observations, $x _ { 1 } - 3 , x _ { 2 } - 3 , \ldots , x _ { 10 } - 3$, then the ordered pair $( \mu , \lambda )$ is equal to:
(1) $( 3,3 )$
(2) $( 6,3 )$
(3) $( 6,6 )$
(4) $( 3,6 )$

jee-main 2020 Q60 View

For the frequency distribution: Variate $( x ) : x _ { 1 } , x _ { 2 } , x _ { 3 } , \ldots , x _ { 15 }$ Frequency $( f ) : f _ { 1 } , f _ { 2 } , f _ { 3 } , \ldots , f _ { 15 }$ where $0 < x _ { 1 } < x _ { 2 } < x _ { 3 } < \ldots < x _ { 15 } = 10$ and $\sum _ { i = 1 } ^ { 15 } f _ { i } > 0$, the standard deviation cannot be
(1) 4
(2) 1
(3) 6
(4) 2

jee-main 2020 Q60 View

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 difference of the remaining two observations is:
(1) 7
(2) 3
(3) 5
(4) 9

jee-main 2020 Q60 View

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 remaining two observations is :
(1) 1
(2) 4
(3) 2
(4) 3

jee-main 2020 Q60 View

If $\sum _ { i = 1 } ^ { n } \left( x _ { i } - a \right) = n$ and $\sum _ { i = 1 } ^ { n } \left( x _ { i } - a \right) ^ { 2 } = n a , ( n , a > 1 )$, then the standard deviation of $n$ observations $x _ { 1 } , x _ { 2 } , \ldots , x _ { n }$ is
(1) $a - 1$
(2) $n \sqrt { ( a - 1 ) }$
(3) $\sqrt { n ( a - 1 ) }$
(4) $\sqrt { ( a - 1 ) }$

jee-main 2020 Q61 View

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:
(1) $x^2 - 10x + 18 = 0$
(2) $2x^2 - 20x + 19 = 0$
(3) $x^2 - 10x + 19 = 0$
(4) $x^2 - 20x + 18 = 0$

jee-main 2020 Q73 View

If the variance of the following frequency distribution:

Class:	$10 - 20$	$20 - 30$	$30 - 40$
Frequency:	2	$x$	2

is 50, then $x$ is equal to $\_\_\_\_$

jee-main 2020 Q74 View

If the variance of the first $n$ natural numbers is 10 and the variance of the first $m$ even natural numbers is 16, then the value of $m + n$ is equal to

jee-main 2021 Q67 View

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 observations are:
(1) 10,11
(2) 3,18
(3) 8,13
(4) 1,20

jee-main 2021 Q67 View

If the mean and variance of six observations $7,10,11,15 , a , b$ are 10 and $\frac { 20 } { 3 }$, respectively, then the value of $| a - b |$ is equal to:
(1) 9
(2) 11
(3) 7
(4) 1

jee-main 2021 Q69 View

Let in a series of $2 n$ 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 observations, the mean and standard deviation of new set become 5 and 20 , respectively. Then the value of $a ^ { 2 } + b ^ { 2 }$ is equal to:
(1) 425
(2) 650
(3) 250
(4) 925

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LFM Stats And Pure

Completing the square and sketching 61

Inequalities 181

Discriminant and conditions for roots 65

Solving quadratics and applications 131

Curve Sketching 228

Factor & Remainder Theorem 61

Polynomial Division & Manipulation 35

Binomial Theorem (positive integer n) 197

Function Transformations 28

Composite & Inverse Functions 211

Partial Fractions 12

Generalised Binomial Theorem 10

Complex Numbers Arithmetic 207

Complex Numbers Argand & Loci 159

Permutations & Arrangements 255

Combinations & Selection 237

Measures of Location and Spread 181

Probability Definitions 212

Tree Diagrams 18

Principle of Inclusion/Exclusion 33

Independent Events 35

Conditional Probability 167

Discrete Probability Distributions 176

Uniform Distribution 3

Binomial Distribution 101

Geometric Distribution 8

Hypergeometric Distribution 9

Negative Binomial Distribution 1

Modelling and Hypothesis Testing 22

Hypothesis test of binomial distributions 2

Data representation 21

Continuous Probability Distributions and Random Variables 322

Continuous Uniform Random Variables 3

Geometric Probability 16

Normal Distribution 87

Approximating Binomial to Normal Distribution 4

Sign Change & Interval Methods 26

Fixed Point Iteration 9

Newton-Raphson method 6