Measures of Dispersion

Interactive Feed

JEE Main 2016

LEVELJEE Main

If the standard deviation of the numbers 2, 3, a and 11 is 3.5, then which of the following is true?

The variance of first 50 even natural numbers is

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 ?

Suppose a population A has 100 observations 101, 102, ..., 200 and another population B has 100 observations 151, 152, ..., 250. If $V_{A}$ and $V_{B}$ represent the variances of the two populations, respectively then $\frac{V _{A}}{V _{B}}$ is

(A)

(B)

\frac{9}{4}

(C)

\frac{4}{9}

(D)

\frac{2}{3}

JEE Main 2005

LEVELBoard

Let $x_{1}, x_{2}, \dots, x_{n}$ be n observations such that $\sum x_{i}^{2} = 400$ and $\sum x_{i} = 80$ . Then the possible value of n among the following is

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?

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 $∣ a ∣$ equals.

(A)

\frac{2}{n}

(B)

2

(C)

(D)

\frac{1}{n}

JEE Main 2003

LEVELBoard

In an experiment with 15 observations on x, the 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. The corrected variance is

Consider any set of 201 observations $x_{1}, x_{2}, \dots, x_{200}, x_{201}$ . It is given that $x_{1} < x_{2} < \dots < x_{200} < x_{201}$ . Then the mean deviation of this set of observations about a point $k$ is minimum when $k$ equals

(A)

(x_{1} + x_{2} + \dots + x_{200} + x_{201}) /201

(B)

x_{1}

(C)

x_{101}

(D)

x_{201}

JEE Advanced 1980

LEVELBoard

Let $S$ be the standard deviation of $n$ observations. Each of the $n$ observations is multiplied by a constant $c$ . Then the standard deviation of the resulting number is

(A)

s

(B)

cs

(C)

s c

In calculating the mean and variance of 10 readings, a student wrongly used the figure 52 for the correct figure of 25. He obtained the mean and variance as 45.0 and 16.0 respectively. Determine the correct mean and variance.

JEE Main 2019 (12 January)

LEVELJEE Main

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 :

(A)

1

(B)

3

(C)

7

(D)

5

JEE Main 2020 (8 January Shift 2)

LEVELJEE Main

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:

JEE Main 2020 - 8 Jan (Evening)

LEVELBoard

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 :

(A)

3.99

(B)

3.98

(C)

4.01

(D)

4.02

JEE Main 2020 - 9 Jan (Morning)

LEVELBoard

For observations $x_{i}$ given $\sum_{i = 1}^{10} (x_{i} - 5) = 10$ and $\sum_{i = 1}^{10} (x_{i} - 5)^{2} = 40$ . If mean and variance of observations $(x_{1} - 3), (x_{2} - 3) \dots (x_{10} - 3)$ is $λ$ & $μ$ respectively then ordered pair $(λ, μ)$ is

(A)

(3, 3)

(B)

(1, 3)

(C)

(3, 1)

(D)

(1, 1)

JEE Main 2020 - 4 Sep (Morning)

LEVELJEE Main

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 :

(A)

9

(B)

3

(C)

7

(D)

5

JEE Main 2021 (27 Aug Shift 1)

LEVELBoard

Let $n$ be an odd natural number such that the variance of $1, 2, 3, 4, \dots, n$ is 14. Then $n$ is equal to .

JEE Main 2021 (26 Aug Shift 2)

LEVELJEE Main

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 $3 + 2 x, 7 + 2 y, x + y$ and $x - y$ is .

JEE Main 2021 (27 July Shift 1)

LEVELBoard

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:

JEE Main 2021 (27 July Shift 2)

LEVELJEE Main

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 respectively. If $x_{3}$ is changed from 8 to 7, then the mean for the new data will be:

(A)

(B)

(C)

\frac{17}{3}

(D)

\frac{16}{3}

JEE Main 2022 (25 June Shift 2)

LEVELJEE Main

If the mean deviation about the mean of the numbers $1, 2, 3, \dots, n$ , where $n$ is odd, is $\frac{5 ( n + 1 )}{n}$ , then $n$ is equal to ______.

JEE Main 2022 (26 June Shift 1)

LEVELJEE Main

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:

JEE Main 2022 (29 July Shift 1)

LEVELJEE Main

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 $(x_{1} + α)^{2}, (x_{2} + α)^{2}, \dots, (x_{20} + α)^{2}$ is 178, then the square of the maximum value of $α$ is equal to

JEE Main 2023 (11 April Shift 2)

LEVELBoard

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

(A)

\frac{7}{3}

(B)

(C)

\frac{8}{3}

(D)

\frac{10}{3}

JEE Main 2023 (13 April Shift 1)

LEVELJEE Main

Let the mean of the data $x Frequency (f) 14324528 7 α 98$ 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 _______.

If the standard deviation of the numbers 2, 3, a and 11 is 3.5, then which of the following is true?

The variance of first 50 even natural numbers is

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 ?

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Let x1​,x2​,…,xn​ be n observations such that ∑xi2​=400 and ∑xi​=80. Then the possible value of n among the following is

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?

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } 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∣ equals.

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Let S be the standard deviation of n observations. Each of the n observations is multiplied by a constant c. Then the standard deviation of the resulting number is

In calculating the mean and variance of 10 readings, a student wrongly used the figure 52 for the correct figure of 25. He obtained the mean and variance as 45.0 and 16.0 respectively. Determine the correct mean and variance.

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 :

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:

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 :

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 :

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Let n be an odd natural number such that the variance of 1,2,3,4,…,n is 14. Then n is equal to .

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } 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 .

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } If the mean and variance of the following data: 6, 10, 7, 13, a, 12, b, 12 are 9 and 437​ respectively, then (a−b)2 is equal to:

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } If the mean deviation about the mean of the numbers 1,2,3,…,n, where n is odd, is n5(n+1)​, then n is equal to ______.

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } 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 25M is equal to:

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } 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

Let $x_{1}, x_{2}, \dots, x_{n}$ be n observations such that $\sum x_{i}^{2} = 400$ and $\sum x_{i} = 80$ . Then the possible value of n among the following is

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 $∣ a ∣$ equals.

Let $S$ be the standard deviation of $n$ observations. Each of the $n$ observations is multiplied by a constant $c$ . Then the standard deviation of the resulting number is

Let $n$ be an odd natural number such that the variance of $1, 2, 3, 4, \dots, n$ is 14. Then $n$ is equal to .

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 $3 + 2 x, 7 + 2 y, x + y$ and $x - y$ is .

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:

If the mean deviation about the mean of the numbers $1, 2, 3, \dots, n$ , where $n$ is odd, is $\frac{5 ( n + 1 )}{n}$ , then $n$ is equal to ______.

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:

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