Statistics

134 questions · Mathematics · JEE Main

Statistics

134 questions · Mathematics · JEE Main

If the mean and the variance of $6, 4, a, 8, b, 12, 10, 13$ are 9 and 9.25 respectively, then $a + b + ab$ is equal to :2025 · 2 Apr · Shift 2 · Q26 · MCQ
Let the Mean and Variance of five observations $x_{1} = 1, x_{2} = 3, x_{3} = a, x_{4} = 7$ and $x_{5} = b, a > b$ , be 5 and 10 respectively. Then the Variance of the observations $n + x_{n}, n = 1, 2, \dots, 5$ is2025 · 3 Apr · Shift 2 · Q37 · MCQ
Let the mean and the standard deviation of the observation $2, 3, 3, 4, 5, 7, a, b$ be 4 and $2$ respectively. Then the mean deviation about the mode of these observations is :2025 · 4 Apr · Shift 2 · Q28 · MCQ
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 $μ$ and $σ$ respectively, then $10 (μ + σ)$ …2025 · 7 Apr · Shift 1 · Q29 · MCQ
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 interval 12-18 and median class frequency 12. If the number of…2025 · 23 Jan · Shift 1 · Q37 · MCQ
The variance of the numbers $8, 21, 34, 47, \dots, 320$ is .2025 · 23 Jan · Shift 2 · Q50 · Numerical
For a statistical data $x_{1}, x_{2}, \dots, x_{10}$ of 10 values, a student obtained the mean as 5.5 and $\sum_{i = 1}^{10} x_{i}^{2} = 371$ . He later found that he had noted two values in the data incorrectly as 4 and 5 ,…2025 · 24 Jan · Shift 1 · Q42 · MCQ
Let $x_{1}, x_{2}, ..., x_{10}$ be ten observations such that $i = 1 \sum 10 (x_{i} - 2) = 30$ , $i = 1 \sum 10 (x_{i} - β)^{2} = 98$ , $β > 2$ , and their variance is $\frac{4}{5}$ . If $μ$ and $σ^{2}$ are respectively…2025 · 29 Jan · Shift 1 · Q38 · MCQ
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 :2024 · 1 Feb · Shift 1 · Q37 · MCQ
Consider 10 observations $x_{1}, x_{2}, \dots, x_{10}$ such that $i = 1 \sum 10 (x_{i} - α) = 2$ and $i = 1 \sum 10 (x_{i} - β)^{2} = 40$ , where $α, β$ are positive integers. Let the mean and the…2024 · 1 Feb · Shift 2 · Q40 · MCQ
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 :2024 · 4 Apr · Shift 1 · Q36 · MCQ
Let the mean and the standard deviation of the probability distribution be $μ$ and $σ$ , respectively. If $σ - μ = 2$ , then $σ + μ$ is equal to . Includes table2024 · 5 Apr · Shift 2 · Q52 · Numerical
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 is2024 · 6 Apr · Shift 1 · Q45 · MCQ
Let $a, b, c \in N$ 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 $\frac{136}{5}$ ,…2024 · 8 Apr · Shift 2 · Q51 · Numerical
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 $4 x + 5 y$ is equal to : Includes table2024 · 9 Apr · Shift 1 · Q39 · MCQ
If the variance of the frequency distribution is 160, then the value of $c \in N$ is Includes table2024 · 9 Apr · Shift 2 · Q43 · MCQ
Let $a_{1}, a_{2}, \dots a_{10}$ be 10 observations such that $k = 1 \sum 10 a_{k} = 50$ and $\forall k < j \sum a_{k} \cdot a_{j} = 1100$ …2024 · 27 Jan · Shift 1 · Q47 · MCQ
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 $μ$ and $σ^{2}$ denote the mean and variance of the correct…2024 · 27 Jan · Shift 2 · Q51 · Numerical
If the mean and variance of the data $65, 68, 58, 44, 48, 45, 60, α, β, 60$ where $α > β$ , are 56 and 66.2 respectively, then $α^{2} + β^{2}$ is equal to .2024 · 29 Jan · Shift 1 · Q52 · Numerical
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 to2024 · 29 Jan · Shift 2 · Q38 · MCQ
Let M denote the median of the following frequency distribution Then 20M is equal to : Includes table2024 · 30 Jan · Shift 1 · Q42 · MCQ
The variance $σ^{2}$ of the data is . Includes table2024 · 30 Jan · Shift 2 · Q56 · Numerical
Let the mean and the variance of 6 observations $a, b, 68, 44, 48, 60$ be $55$ and $194$ , respectively. If $a > b$ , then $a + 3 b$ is2024 · 31 Jan · Shift 2 · Q50 · MCQ
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 :2023 · 1 Feb · Shift 1 · Q29 · MCQ
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 $\overset{x}{ˉ}$ , then $\overset{x}{ˉ} + x_{6}$ is equal to :2023 · 1 Feb · Shift 2 · Q24 · MCQ
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 $σ^{2}$ …2023 · 6 Apr · Shift 1 · Q27 · MCQ
If the mean and variance of the frequency distribution are 9 and 15.08 respectively, then the value of $α^{2} + β^{2} - α β$ is . Includes table2023 · 6 Apr · Shift 2 · Q37 · Numerical
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 .2023 · 8 Apr · Shift 1 · Q42 · Numerical
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…2023 · 8 Apr · Shift 2 · Q27 · MCQ
If the mean of the frequency distribution is 28, then its variance is . Includes table2023 · 10 Apr · Shift 1 · Q42 · Numerical
Let $μ$ be the mean and $σ$ be the standard deviation of the distribution where $\sum f_{i} = 62$ . If $[x]$ denotes the greatest integer $\leq x$ , then $[μ^{2} + σ^{2}]$ is equal to : Includes table2023 · 10 Apr · Shift 2 · Q28 · MCQ
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…2023 · 11 Apr · Shift 1 · Q31 · MCQ
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 :2023 · 11 Apr · Shift 2 · Q31 · MCQ
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 co-prime. If the mean of their reciprocals is $\frac{31}{40}$ …2023 · 12 Apr · Shift 1 · Q42 · Numerical
Let the mean of the data be 5. If $m$ and $σ^{2}$ are respectively the mean deviation about the mean and the variance of the data, then $\frac{3 α}{m + σ ^{2}}$ is equal to Includes table2023 · 13 Apr · Shift 1 · Q38 · Numerical
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 …2023 · 13 Apr · Shift 2 · Q35 · Numerical
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 :2023 · 15 Apr · Shift 1 · Q30 · MCQ
Let the six numbers $a_{1}, a_{2}, a_{3}, a_{4}, a_{5}, a_{6}$ , be in A.P. and $a_{1} + a_{3} = 10$ . If the mean of these six numbers is $\frac{19}{2}$ and their variance is $σ^{2}$ , then 8 $σ^{2}$ is equal to :2023 · 24 Jan · Shift 2 · Q33 · MCQ
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 of the marks is 10.2, then their new variance is equal to :2023 · 25 Jan · Shift 1 · Q27 · MCQ
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 apples. If $μ$ and $σ^{2}$ represent mean and variance of…2023 · 29 Jan · Shift 1 · Q24 · MCQ
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 $σ^{2}$ is the variance of all the observations in $X \cup Y$ ,…2023 · 29 Jan · Shift 2 · Q40 · Numerical
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 .2023 · 30 Jan · Shift 1 · Q39 · Numerical
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 :2023 · 30 Jan · Shift 2 · Q26 · MCQ
If the variance of the frequency distribution is 3, then $α$ is equal to . Includes table2023 · 31 Jan · Shift 1 · Q47 · Numerical
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 $B$ of $n$ students be respectively 55 and 30 $- α$ . If the mean and…2023 · 31 Jan · Shift 2 · Q28 · MCQ
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 :2022 · 25 Jul · Shift 2 · Q35 · MCQ
If the mean deviation about the mean of the numbers 1, 2, 3, .........., n, where n is odd, is $\frac{5 ( n + 1 )}{n}$ , then n is equal to .2022 · 25 Jun · Shift 2 · Q41 · Numerical
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 $σ$ is the standard deviation of the data after omitting the two wrong…2022 · 26 Jul · Shift 2 · Q36 · Numerical
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 :2022 · 26 Jun · Shift 1 · Q31 · MCQ
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 observations is 70. If the correct mean is 16, then the correct…2022 · 26 Jun · Shift 2 · Q36 · MCQ
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 standard deviation is .2022 · 27 Jul · Shift 1 · Q40 · Numerical
The mean and variance of the data 4, 5, 6, 6, 7, 8, x, y, where x < y, are 6 and $\frac{9}{4}$ respectively. Then $x^{4} + y^{2}$ is equal to :2022 · 27 Jun · Shift 2 · Q33 · MCQ
Let $x_{1}, x_{2}, x_{3}, \dots, x_{20}$ 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 $(x_{i} - i)^{2}$ . If $\overset{x}{ˉ}$ is the mean of new…2022 · 28 Jul · Shift 1 · Q44 · Numerical
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 correct variance is equal to .2022 · 28 Jun · Shift 1 · Q37 · Numerical
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 gets less than 50 marks, then in worst case, the number of…2022 · 28 Jun · Shift 2 · Q42 · Numerical
Let the mean and the variance of 20 observations $x_{1}, x_{2}, \dots, x_{20}$ be 15 and 9 , respectively. For $α \in R$ , if the mean of $(x_{1} + α)^{2}, (x_{2} + α)^{2}, \dots, (x_{20} + α)^{2}$ …2022 · 29 Jul · Shift 1 · Q41 · Numerical
Let the mean and the variance of 5 observations x1, x2, x3, x4, x5 be $\frac{24}{5}$ and $\frac{194}{25}$ respectively. If the mean and variance of the first 4 observation are $\frac{7}{2}$ and a respectively, then (4a + x5) is equal to:2022 · 29 Jun · Shift 1 · Q35 · MCQ
The number of values of a $\in$ N such that the variance of 3, 7, 12, a, 43 $-$ a is a natural number is :2022 · 29 Jun · Shift 2 · Q34 · MCQ
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?2021 · 16 Mar · Shift 1 · Q32 · MCQ
Consider the statistics of two sets of observations as follows : If the variance of the combined set of these two observations is $\frac{17}{9}$ , then the value of n is equal to . Includes table2021 · 16 Mar · Shift 2 · Q44 · Numerical
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 into each of first 2n numbers, and subtracting 1 from each of…2021 · 17 Mar · Shift 2 · Q40 · Numerical
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…2021 · 18 Mar · Shift 1 · Q44 · Numerical
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 standard deviation of new set become 5 and 20, respectively.…2021 · 18 Mar · Shift 2 · Q31 · MCQ
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 :2021 · 20 Jul · Shift 1 · Q23 · MCQ
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 :2021 · 20 Jul · Shift 2 · Q34 · MCQ
Consider the following frequency distribution : If mean = $\frac{309}{22}$ and median = 14, then the value (a $-$ b)2 is equal to . Includes table2021 · 22 Jul · Shift 2 · Q41 · Numerical
If the variance of 10 natural numbers 1, 1, 1, ....., 1, k is less than 10, then the maximum possible value of k is .2021 · 24 Feb · Shift 2 · Q35 · Numerical
Consider the following frequency distribution : If the sum of all frequencies is 584 and median is 45, then | $α - β$ | is equal to . Includes table2021 · 25 Jul · Shift 1 · Q39 · Numerical
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 $13.44$ , then the standard deviation of the second sample is :2021 · 25 Jul · Shift 2 · Q25 · MCQ
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 $α$ and $β$ are the mean and standard deviation…2021 · 26 Aug · Shift 1 · Q23 · MCQ
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 .2021 · 26 Aug · Shift 2 · Q44 · Numerical
Let X1, X2, ......., X18 be eighteen observations such that $i = 1 \sum 18 (X_{i} - α) = 36$ and $i = 1 \sum 18 (X_{i} - β)^{2} = 90$ , where $α$ and $β$ are distinct real numbers. If the…2021 · 26 Feb · Shift 2 · Q46 · Numerical
Let n be an odd natural number such that the variance of 1, 2, 3, 4, ......, n is 14. Then n is equal to .2021 · 27 Aug · Shift 1 · Q39 · Numerical
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 also 2. The average marks of all 50 candidates is 15. If $μ$ …2021 · 27 Aug · Shift 2 · Q40 · Numerical
If the mean and variance of the following data : 6, 10, 7, 13, a, 12, b, 12 are 9 and $\frac{37}{4}$ respectively, then (a $-$ b)2 is equal to :2021 · 27 Jul · Shift 1 · Q23 · MCQ
Let the mean and variance of the frequency distribution $x : f : x_{1} = 2 4 x_{2} = 6 4 x_{3} = 8 α x_{4} = 9 β$ be 6 and 6.8…2021 · 27 Jul · Shift 2 · Q28 · MCQ
The mean of 10 numbers 7 $\times$ 8, 10 $\times$ 10, 13 $\times$ 12, 16 $\times$ 14, ....... is .2021 · 31 Aug · Shift 1 · Q40 · Numerical
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 :2021 · 31 Aug · Shift 2 · Q36 · MCQ
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 :2020 · 2 Sep · Shift 1 · Q36 · MCQ
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 .2020 · 2 Sep · Shift 2 · Q35 · Numerical
For the frequency distribution : Variate (x) : x1 x2 x3 .... x15 Frequency (f) : f1 f2 f3 ...... f15 where 0 < x1 < x2 < x3 < ... < x15 = 10 and $i = 1 \sum 15 f_{i}$ > 0, the standard deviation cannot be :2020 · 3 Sep · Shift 1 · Q19 · MCQ
Let xi (1 $\leq$ i $\leq$ 10) be ten observations of a random variable X. If $i = 1 \sum 10 (x_{i} - p) = 3$ and $i = 1 \sum 10 (x_{i} - p)^{2} = 9$ where 0 $e$ p $\in$ R, then…2020 · 3 Sep · Shift 2 · Q36 · MCQ
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 :2020 · 4 Sep · Shift 1 · Q29 · MCQ
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 2020 · 4 Sep · Shift 2 · Q23 · Numerical
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 :2020 · 5 Sep · Shift 1 · Q32 · MCQ
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 :2020 · 5 Sep · Shift 2 · Q19 · MCQ
If $i = 1 \sum n (x_{i} - a) = n$ and $i = 1 \sum n (x_{i} - a)^{2} = na$ (n, a > 1) then the standard deviation of n observations x1 , x2 , ..., xn is :2020 · 6 Sep · Shift 1 · Q31 · MCQ
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 $\frac{728}{2 ^{n}}$ , then n is equal to .2020 · 6 Sep · Shift 2 · Q27 · Numerical
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 .2020 · 7 Jan · Shift 1 · Q31 · Numerical
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 .2020 · 7 Jan · Shift 2 · Q27 · Numerical
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 $e$ 0 and q $e$ 0. If the new mean and new s.d. become half of their…2020 · 8 Jan · Shift 1 · Q33 · MCQ
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 is2020 · 8 Jan · Shift 2 · Q24 · MCQ
Let the observations xi (1 $\leq$ i $\leq$ 10) satisfy the equations, $i = 1 \sum 10 (x_{1} - 5)$ = 10 and $i = 1 \sum 10 (x_{1} - 5)^{2}$ = 40. If $μ$ and $λ$ are the mean…2020 · 9 Jan · Shift 1 · Q41 · MCQ
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 remaining two observations is :2019 · 8 Apr · Shift 1 · Q33 · MCQ
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 is2019 · 8 Apr · Shift 2 · Q39 · MCQ
If the standard deviation of the numbers –1, 0, 1, k is $5$ where k > 0, then k is equal to2019 · 9 Apr · Shift 1 · Q23 · MCQ
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 to2019 · 9 Apr · Shift 2 · Q29 · MCQ
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 height of these six students is :2019 · 9 Jan · Shift 1 · Q36 · MCQ
A data consists of n observations : x1, x2, . . . . . . ., xn. If $i = 1 \sum n (x_{i} + 1)^{2} = 9 n$ and $i = 1 \sum n (x_{i} - 1)^{2} = 5 n,$ then the standard deviation of this…2019 · 9 Jan · Shift 2 · Q34 · MCQ
If for some x $\in$ R, the frequency distribution of the marks obtained by 20 students in a test is : then the mean of the marks is Includes table2019 · 10 Apr · Shift 1 · Q35 · MCQ
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 – 4)2 is :2019 · 10 Apr · Shift 2 · Q32 · MCQ
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 -2019 · 10 Jan · Shift 1 · Q25 · MCQ
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 and –50 is equal to2019 · 10 Jan · Shift 2 · Q39 · MCQ
The outcome of each of 30 items was observed; 10 items gave an outcome $\frac{1}{2}$ – d each, 10 items gave outcome $\frac{1}{2}$ each and the remaining 10 items gave outcome $\frac{1}{2}$ + d each. If the variance of this outcome data is $\frac{4}{3}$ …2019 · 11 Jan · Shift 1 · Q27 · MCQ
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 of these is 2,000 ; then the standard deviation of this data is :2019 · 12 Apr · Shift 1 · Q38 · MCQ
If the sum of the deviations of 50 observations from 30 is 50, then the mean of these observations is :2019 · 12 Jan · Shift 1 · Q23 · MCQ
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 :2019 · 12 Jan · Shift 2 · Q34 · MCQ
The mean of set of 30 observations is 75. If each observation is multiplied by a non-zero number $λ$ and then each of them is decreased by 25, their mean remains the same. Then $λ$ is equal to :2018 · 15 Apr · Shift 1 · Q37 · MCQ
If the mean of the data : 7, 8, 9, 7, 8, 7, $λ$ , 8 is 8, then the variance of this data is :2018 · 15 Apr · Shift 2 · Q31 · MCQ
The mean and the standard deviation(s.d.) of five observations are9 and 0, respectively. If one of the observations is changed such that the mean of the new set of five observations becomes 10, then their s.d. is :2018 · 16 Apr · Shift 1 · Q41 · MCQ
If $i = 1 \sum 9 (x_{i} - 5) = 9$ and $i = 1 \sum 9 (x_{i} - 5)^{2} = 45$ , then the standard deviation of the 9 items $x_{1}, x_{2}, ......., x_{9}$ is2018 · Shift 0 · Q35 · MCQ
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 mean age of the teachers in this school is 39 years, then the age (in years) of the newly…2017 · 8 Apr · Shift 1 · Q39 · MCQ
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 incorrect. If the incorrect observations are omitted, then the variance of the remaining…2017 · 9 Apr · Shift 1 · Q32 · MCQ
If the mean deviation of the numbers 1, 1 + d, ..., 1 +100d from their mean is 255, then a value of d is :2016 · 9 Apr · Shift 1 · Q35 · MCQ
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 data is :2016 · 10 Apr · Shift 1 · Q31 · MCQ
If the standard deviation of the numbers 2, 3, a and 11 is 3.5, then which of the following is true?2016 · Shift 0 · Q23 · MCQ
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 and 5 are added to the data, then the mean of the resultant data, is :2015 · Shift 0 · Q24 · MCQ
The variance of first 50 even natural numbers is2014 · Shift 0 · Q25 · MCQ
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 following statistical measures will not change even after the grace marks were given?2013 · Shift 0 · Q28 · MCQ
Let x1, x2,........., xn be n observations, and let $\overline{x}$ be their arithematic mean and $σ^{2}$ be their variance. Statement 1 : Variance of 2x1, 2x2,......., 2xn is 4 $σ^{2}$ . Statement 2 : : Arithmetic mean of 2x1,…2012 · Shift 0 · Q24 · MCQ
If the mean deviation about the median of the numbers a, 2a,........., 50a is 50, then |a| equals2011 · Shift 0 · Q29 · MCQ
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 variance of the combined data set is2010 · Shift 0 · Q27 · MCQ
Statement - 1 : The variance of first n even natural numbers is $\frac{n ^{2} - 1}{4}$ Statement - 2 : The sum of first n natural numbers is $\frac{n ( n + 1 )}{2}$ and the sum of squares of first n natural numbers is $\frac{n ( n + 1 ) ( 2 n + 1 )}{6}$ …2009 · Shift 0 · Q26 · MCQ
If the mean deviation of number 1, 1 + d, 1 + 2d,........, 1 + 100d from their mean is 255, then the d is equal to2009 · Shift 0 · Q27 · MCQ
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?2008 · Shift 0 · Q30 · MCQ
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 class is2007 · Shift 0 · Q39 · MCQ
Suppose a population A has 100 observations 101, 102,........, 200, and another population B has 100 observations 151, 152,......., 250. If VA and VB represent the variances of the two populations, respectively, then $\frac{V _{A}}{V _{B}}$ …2006 · Shift 0 · Q52 · MCQ
If in a frequency distribution, the mean and median are 21 and 22 respectively, then its mode is approximately :2005 · Shift 0 · Q66 · MCQ
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 following is2005 · Shift 0 · Q67 · MCQ
Consider the following statements: (a) Mode can be computed from histogram (b) Median is not independent of change of scale (c) Variance is independent of change of origin and scale. Which of these is/are correct?2004 · Shift 0 · Q73 · MCQ
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 $∣ a ∣$ equals2004 · Shift 0 · Q74 · MCQ
In an experiment with 15 observations on $x$ , then following results were available: $\sum x^{2} = 2830$ , $\sum x = 170$ One observation that was 20 was found to be wrong and was replaced by the correct value 30. Then the corrected…2003 · Shift 0 · Q74 · MCQ
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 set :2003 · Shift 0 · Q75 · MCQ
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 the average marks of the girls?2002 · Shift 0 · Q63 · MCQ