JEE MAIN · MATHEMATICS · STATISTICS
JEE Main Statistics Questions & Solutions
91 solved questions on Statistics, ranging from easy to JEE-Advanced-flavour hard. Click any to see the full solution.
91 solved questions on Statistics, ranging from easy to JEE-Advanced-flavour hard. Click any to see the full solution.
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) then the standard deviation of n…
View solution →The mean and variance of the data 4, 5, 6, 6, 7, 8, x, y, where x
View solution →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_____.
View solution →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 _______.
View solution →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 true?
View solution →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_______.
View solution →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…
View solution →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 $\sum\limits_{i = 1}^{10} {{{\left(…
View solution →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 reduced by q, where p $\ne$ 0…
View solution →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.…
View solution →Let the mean of 6 observations $1,2,4,5, \mathrm{x}$ and $\mathrm{y}$ be 5 and their variance be 10 . Then their mean deviation about the mean is equal to :
View solution →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 $\mu$…
View solution →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…
View solution →Consider the following frequency distribution : .tg {border-collapse:collapse;border-spacing:0;} .tg td{border-color:black;border-style:solid;border-width:1px;font-family:Arial,…
View solution →The frequency distribution of the age of students in a class of 40 students is given below. .tg {border-collapse:collapse;border-spacing:0;} .tg…
View solution →The mean of 10 numbers 7 $\times$ 8, 10 $\times$ 10, 13 $\times$ 12, 16 $\times$ 14, ....... is ____________.
View solution →Let n be an odd natural number such that the variance of 1, 2, 3, 4, ......, n is 14. Then n is equal to _____________.
View solution →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 as 25 instead of 35. if…
View solution →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…
View solution →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 to :
View solution →Let the positive numbers $a_{1}, a_{2}, a_{3}, a_{4}$ and $a_{5}$ be in a G.P. Let their mean and variance be $\frac{31}{10}$ and $\frac{m}{n}$ respectively, where $m$ and $n$ are…
View solution →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 of Y are 17 and 216 respectively then a + b is equal…
View solution →Consider 10 observations $x_1, x_2, \ldots, x_{10}$ such that $\sum\limits_{i=1}^{10}\left(x_i-\alpha\right)=2$ and $\sum\limits_{i=1}^{10}\left(x_i-\beta\right)^2=40$, where…
View solution →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 :
View solution →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 :
View solution →Let $\alpha, \beta \in \mathbf{R}$. 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…
View solution →Let the mean of the data .tg {border-collapse:collapse;border-spacing:0;} .tg td{border-color:black;border-style:solid;border-width:1px;font-family:Arial,…
View solution →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 of the first 4 observation are ${7…
View solution →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 observation. Then, the correct…
View solution →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 mean of…
View solution →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 :
View solution →The number of values of a $\in$ N such that the variance of 3, 7, 12, a, 43 $-$ a is a natural number is :
View solution →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 :
View solution →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 standard deviation $\sqrt…
View solution →Consider the following frequency distribution : .tg {border-collapse:collapse;border-spacing:0;} .tg td{border-color:black;border-style:solid;border-width:1px;font-family:Arial,…
View solution →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…
View solution →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 $3 x-2 y$ is equal to _____________.
View solution →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 of correct and incorrect…
View solution →Let the mean and variance of the frequency distribution$$\matrix{ {x:} & {{x_1} = 2} & {{x_2} = 6} & {{x_3} = 8} & {{x_4} = 9} \cr {f:} & 4 & 4 & \alpha & \beta \cr } $$be 6 and…
View solution →The variance $\sigma^2$ of the data .tg {border-collapse:collapse;border-spacing:0;} .tg td{border-color:black;border-style:solid;border-width:1px;font-family:Arial,…
View solution →Let $\mu$ be the mean and $\sigma$ be the standard deviation of the distribution .tg {border-collapse:collapse;border-spacing:0;} .tg…
View solution →Let the mean and the standard deviation of the probability distribution .tg {border-collapse:collapse;border-spacing:0;} .tg…
View solution →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…
View solution →If the mean and variance of the frequency distribution .tg {border-collapse:collapse;border-spacing:0;} .tg…
View solution →Let $9=x_{1}
View solution →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 marks obtained by 30 girls is…
View solution →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 $\frac{19}{2}$ and their variance is $\sigma^2$,…
View solution →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 their respective means and $\sigma^2$ is…
View solution →Marks obtains by all the students of class 12 are presented in a freqency distribution with classes of equal width. Let the median of this grouped data be 14 with median class…
View solution →If the mean and the variance of $6,4, a, 8, b, 12,10,13$ are 9 and 9.25 respectively, then $a+b+a b$ is equal to :
View solution →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 ______________.
View solution →Let X1, X2, ......., X18 be eighteen observations such that $\sum\limits_{i = 1}^{18} {({X_i} - } \alpha ) = 36$ and $\sum\limits_{i = 1}^{18} {({X_i} - } \beta {)^2} = 90$, where…
View solution →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 $-$ y is ______________.
View solution →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\limits_{i = 1}^{10} {{{\left( {{x_1} -…
View solution →If the variance of the frequency distribution .tg {border-collapse:collapse;border-spacing:0;} .tg td{border-color:black;border-style:solid;border-width:1px;font-family:Arial,…
View solution →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 observations, the mean and…
View solution →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 denote the number of rotten…
View solution →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 recorded. If $\sigma$ is the…
View solution →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…
View solution →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 _________.
View solution →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…
View solution →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 :
View solution →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 is :
View solution →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 misread as 5. Then, the…
View solution →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 is constructed by adding 1…
View solution →Let $S$ be the set of all values of $a_1$ for which the mean deviation about the mean of 100 consecutive positive integers $a_1, a_2, a_3, \ldots ., a_{100}$ is 25 . Then $S$ is :
View solution →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…
View solution →If the mean of the frequency distribution .tg {border-collapse:collapse;border-spacing:0;} .tg td{border-color:black;border-style:solid;border-width:1px;font-family:Arial,…
View solution →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 ${{728} \over {{2^n}}}$, then n…
View solution →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 constructed replacing each $x_{i}$ by…
View solution →If the variance of 10 natural numbers 1, 1, 1, ....., 1, k is less than 10, then the maximum possible value of k is ________.
View solution →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…
View solution →Let the mean and the variance of 6 observations $a, b, 68,44,48,60$ be $55$ and $194$, respectively. If $ab$, then $a+3 b$ is
View solution →Consider the statistics of two sets of observations as follows : Size Mean Variance Observation I 10 2 2 Observation II n 3 1 If the variance of the combined set of these two…
View solution →For the frequency distribution : Variate (x) : x1 x2 x3 .... x15 Frequency (f) : f1 f2 f3 ...... f15 where 0 < x1 < x2 < x3 < ... < x15 = 10 and $\sum\limits_{i = 1}^{15} {{f_i}}$…
View solution →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 :
View solution →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…
View solution →Let $\mathrm{a}, \mathrm{b}, \mathrm{c} \in \mathbf{N}$ and $\mathrm{a}
View solution →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 examination if he/she…
View solution →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…
View solution →The variance of the numbers $8,21,34,47, \ldots, 320$ is _______.
View solution →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 from 8 to 12. If the new mean…
View solution →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 marks of class $B$ of $n$…
View solution →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 :
View solution →Let $\mathrm{a}_1, \mathrm{a}_2, \ldots \mathrm{a}_{10}$ be 10 observations such that $\sum\limits_{\mathrm{k}=1}^{10} \mathrm{a}_{\mathrm{k}}=50$ and $\sum\limits_{\forall…
View solution →Let M denote the median of the following frequency distribution .tg {border-collapse:collapse;border-spacing:0;} .tg…
View solution →For a statistical data $\mathrm{x}_1, \mathrm{x}_2, \ldots, \mathrm{x}_{10}$ of 10 values, a student obtained the mean as 5.5 and $\sum_{i=1}^{10} x_i^2=371$. He later found that…
View solution →Let $x_1, x_2, ..., x_{10}$ be ten observations such that $\sum\limits_{i=1}^{10} (x_i - 2) = 30$, $\sum\limits_{i=1}^{10} (x_i - \beta)^2 = 98$, $\beta 2$, and their variance is…
View solution →Let the Mean and Variance of five observations $x_1=1, x_2=3, x_3=a, x_4=7$ and $x_5=\mathrm{b}, a\mathrm{b}$, be 5 and 10 respectively. Then the Variance of the observations…
View solution →Let the mean and the standard deviation of the observation $2,3,3,4,5,7, a, b$ be 4 and $\sqrt{2}$ respectively. Then the mean deviation about the mode of these observations is :
View solution →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…
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