Statistics — JEE Main PYQs

Let the mean and variance of 7 observations $2,4,10,x,12,14,y,x>y$, be 8 and 16 respectively. Two numbers are chosen from $\{1,2,3,\mathrm{x}-4,\mathrm{y},5\}$ one after another without replacement, then the probability, that the smaller number among the two chosen num …

If the mean deviation about the median of the numbers $k,2k,3k,\dots ,1000k$ is 500, then $k^2$ is equal to :

Let the mean and variance of 8 numbers $-10,-7,-1,x,y,9,2,16$ be $\frac{7}{2}$ and $\frac{293}{4}$, respectively. Then the mean of 4 numbers $x,y,x+y+1,|x-y|$ is:

If the mean and the variance of the data

\begin{tabular}{|l|c|c|c|c|}
\hline Class & $4-8$ & $8-12$ & $12-16$ & $16-20$ \\
\hline Frequency & 3 & $\lambda$ & 4 & 7 \\
\hline
\end{tabular}

are $\mu$ and 19 respectively, then the value of $\lambda +\mu$ is

The mean and variance of a data of 10 observations are 10 and 2, respectively. If an observation $\alpha$ in this data is replaced by $\beta$, then the mean and variance become 10.1 and 1.99, respectively. Then $\alpha +\beta$ equals.

Let $\mathrm{X}=\{\mathrm{x}\in \mathbb{N}:1\le \mathrm{x}\le 19\}$ and for some $\mathrm{a},\mathrm{b}\in \mathbb{R}$, $\mathrm{Y}=\{\mathrm{ax}+\mathrm{b}:\mathrm{x}\in \mathrm{X}\}$. If the mean and variance of the elements of Y are 30 and 750, respectively, th …

The mean and variance of 10 observations are 9 and 34.2, respectively. If 8 of these observations are $2,3,5,10,11,13,15,21$, then the mean deviation about the median of all the 10 observations is

If the mean of the data

is 21, then k is one of the roots of the equation :

For 10 observations ${\mathrm{x}}_1,{\mathrm{x}}_2,\dots .,{\mathrm{x}}_{10}$, if ${\sum }_{\mathrm{i}=1}^{10}{\left({\mathrm{x}}_{\mathrm{i}}+2\right)}^2=180$ and ${\sum }_{\mathrm{i}=1}^{10}{\left({\mathrm{x}}_{\mathrm{i}}-1\right)}^2=90$, then their standard deviation is :

Suppose that the mean and median of the nonnegative numbers 21, 8, 17, a, $51,103,\mathrm{b},13,67$, $(\mathrm{a}>\mathrm{b})$, are 40 and 21, respectively. If the mean deviation about the median is 26 , then 2 a is equal to :

The mean deviation about the mean for the data

is equal to :

Let the mean and the variance of seven observations $2,4,\alpha ,8,\beta ,12,14,\alpha <\beta$, be 8 and 16 respectively. Then the quadratic equation whose roots are $3\alpha +2$ and $2\beta +1$ is :

A data consists of 20 observations $x_1,x_2,\dots ,x_{20}$. If ${\sum }_{i=1}^{20}(x_i+5{)}^2=2500$ and ${\sum }_{i=1}^{20}(x_i-5{)}^2=100$, then the ratio of mean to standard deviation of this data is:

A set of four observations has mean 1 and variance 13. Another set of six observations has mean 2 and variance 1. Then, the variance of all these 10 observations is equal to :

The mean and variance of $n$ observations are 8 and 16, respectively. If the sum of the first ($n-1$) observations is 48 and the sum of squares of the first ($\mathrm{n}-1$) observations is 496, then the value of n is :

Marks obtains by all the students of class 12 are presented in a frequency distribution with classes of equal width. Let the median of this grouped data be 14 with median class interval 12-18 and median class frequency 12. If the number of students whose marks are less than 12 is …

The variance of the numbers $8,21,34,47,\dots ,320$, is ______.

Let ${\mathrm{x}}_1,{\mathrm{x}}_2,\dots \dots {\mathrm{x}}_{10}$ be ten observations such that ${\sum }_{i=1}^{10}\left(x_i-2\right)=30,{\sum }_{i=1}^{10}{\left(x_i-\beta \right)}^2=98,\beta >2$ and their variance is $\frac{4}{5}$. If $\mu$ and ${\sigma }^2$ are respectively the …

For a statistical data ${\mathrm{x}}_1,{\mathrm{x}}_2,\dots ,{\mathrm{x}}_{10}$ of 10 values, a student obtained the mean as 5.5 and ${\sum }_{\mathrm{i}=1}^{10}{\mathrm{x}}_{\mathrm{i}}^2=371$. He later found that he had noted two values in the data incorrectly as 4 and 5, instea …

If the mean and the variance of $6,4,\mathrm{a},8,\mathrm{b},12,10$, 13 are 9 and 9.25 respectively, then $\mathrm{a}+\mathrm{b}+\mathrm{ab}$ is equal to:

Let the Mean and Variance of five observations ${\mathrm{x}}_1=1,{\mathrm{x}}_2=3,{\mathrm{x}}_3=\mathrm{a},{\mathrm{x}}_4=7$ and ${\mathrm{x}}_5=\mathrm{b},\mathrm{a}>\mathrm{b}$, be 5 and 10 respectively. Then the Variance of the observations …

Let the mean and the standard deviation of the observation $2,3,3,4,5,7,\mathrm{a},\mathrm{b}$ be 4 and $\sqrt{2}$ respectively. Then the mean deviation about the mode of these observations is:

The mean and standard deviation of 100 observations are 40 and 5.1, respectively. By mistake one observation is taken as 50 instead of 40. If the correct mean and the correct standard deviation are $\mu$ and $\sigma$ respectively, then $10(\mu +\sigma )$ is equal to

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

Let the mean and the standard deviation of the probability distribution $x:\alpha ,1,0,-3$; $P(x):\frac{1}{3},K,\frac{1}{6},\frac{1}{4}$ be $\mu$ and $\sigma$, respectively. If $\sigma -\mu =2$, then $\sigma +\mu$ is equal to ____ .

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

Let $a,b,c\in \mathbb{N}$ and $a<b<c$. Let the mean, the mean deviation about the mean and the variance of the 5 observations $9,25,a,b,c$ be 18, 4 and $\frac{136}{5}$, respectively. Then $2a+b-c$ is equal to ______.

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

If the mean deviation about the median is 1.25 , then …

If the variance of the frequency distribution is 160, then the value of $\mathrm{c}\in \mathrm{N}$ is

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

Let the mean and the variance of 6 observation a, b, 68, 44, 48, 60 be 55 and 194, respectively if $\mathrm{a}>\mathrm{b}$, then $\mathrm{a}+3\mathrm{b}$ is

Let M denote the median of the following frequency distribution.

Then 20M is equal to:

The mean and standard deviation of 15 observations were found to be 12 and 3 respectively. On rechecking it was found that an observation was read as 10 in place of 12 . If $\mu$ and ${\sigma }^2$ denote the mean and variance of the correct observations respectively, then …

Let $a_1,a_2,\dots ..a_{10}$ be 10 observations such that ${\sum }_{\mathrm{k}=1}^{10}{\mathrm{a}}_{\mathrm{k}}=50$ and ${\sum }_{\forall \mathrm{k}<\mathrm{j}}{\mathrm{a}}_{\mathrm{k}}\cdot {\mathrm{a}}_{\mathrm{j}}=1100$. Then the standard deviation of …

Consider 10 observation ${\mathrm{x}}_1,{\mathrm{x}}_2,\dots ,{\mathrm{x}}_{10}$. such that ${\sum }_{i=1}^{10}(x_i-\alpha )=2$ and ${\sum }_{i=1}^{10}(x_i-\beta {)}^2=40$, where $\alpha ,\beta$ are positive integers. Let the mean and the variance of the observations be …

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 :

If the mean and variance of the data $65,68,58,44,48,45,60,\alpha ,\beta ,60$ where $\alpha >\beta$ are $56$ and $66.2$ respectively, then ${\alpha }^2+{\beta }^2$ is equal to

The variance ${\sigma }^2$ of the data

is ______.

If the mean and variance of the frequency distribution

are 9 and 15.08 respectively, then the value of …

Let the mean and variance of 8 numbers $x,y,10,12,6,12,4,8$ be 9 and 9.25 respectively. If $x>y$, then $3x-2y$ is equal to ______.

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 ${\sigma }^2$ respectively. If the variance of all the 30 numbers in the two sets is 13 , then ${\sigma }^2$ is equal to

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 $\frac{\mathrm{m}}{\mathrm{n}}$, where m and n are co-pri …

Let $\mu$ be the mean and $\sigma$ be the standard deviation of the distribution

\begin{tabular}{|l|l|l|l|l|l|l|}
\hline ${\mathrm{x}}_{\mathrm{i}}$ & 0 & 1 & 2 & 3 & 4 & 5 \\
\hline ${\mathrm{f}}_{\mathrm{i}}$ & $\mathrm{k}+2$ & 2 k & ${\mathrm{k}}^2-1$ & ${\mathrm{k}}^2-1$ & …

If the mean of the frequency distribution

\begin{tabular}{|l|l|l|l|l|l|}
\hline Class: & $0-10$ & $10-20$ & $20-30$ & $30-40$ & $40-50$ \\
\hline Frequency & 2 & 3 & x & 5 & 4 \\
\hline
\end{tabular}

is 28 , then its variance is ____.

The mean and standard deviation of the marks of 10 students were found to be 50 and 12 respectively. Later, it was observed that two marks 20 and 25 were wrongly read as 45 and 50 respectively. Then the correct variance is ______.

Let the mean of the data

be 5. If $m$ and ${\sigma }^2$ are respectively the mean deviation about the mean and the variance of the data, then $\frac{3\alpha }{m+{\sigma }^2}$ is equal …

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:

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

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 eac …

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 remaining 6 observation, then $a+3b-5$ is equal to ____.