Measures of Dispersion: JEE Questions & Solutions

If the mean deviation about the median of the numbers k, 2k, 3k, …, 1000k is 500, then k² is equal to

Let the mean and variance of 8 numbers -10, -7, -1, x, y, 9, 2, 16 be 7/2 and 293/4, respectively. Then the mean of 4 numbers x, y, x+y+1,…

Let X={x∈ℕ:1≤ x≤19} and for some a,b∈ℝ, Y={ax+b:x∈ X}. If the mean and variance of the elements of Y are 30 and 750 respectively, then the…

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…

The variance of the numbers 8, 21, 34, 47, …, 320, is:

For a statistical data x₁, x₂, …, x₁₀ of 10 values, a student obtained the mean as 5.5 and Σ_(i=1)¹⁰ xᵢ² = 371. He later found that he had…

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:

Let the Mean and Variance of five observations xᵢ, i = 1, 2, 3, 4, 5 be 5 and 10 respectively. If three observations are x₁ = 1, x₂ = 3, x₃…

Let the mean and the standard deviation of the observations 2, 3, 3, 4, 5, 7, a, b be 4 and √2 respectively. Then the mean deviation about…

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.…

Let a₁, a₂, …, a₁₀ be 10 observations with Σ a_k = 50 and Σ (a_k · a_j) = 1100. Find the standard deviation.

The mean and standard deviation of 15 observations were found to be 12 and 3 respectively. On rechecking, it was found that an observation…

The variance σ² of the data is: xᵢ: 0, 1, 5, 6, 10, 12, 17 fᵢ: 3, 2, 3, 2, 6, 3, 3

Let the median and the mean deviation about the median of 7 observations 170, 125, 230, 190, 210, a, b be 170 and 205/7 respectively. Then…

The mean and standard deviation of 20 observations are found to be 10 and 2, respectively. On rechecking, an observation was mistakenly…

If the variance of the frequency distribution given below is 160, then the value of c ∈ ℕ is: | x | c | 2c | 3c | 4c | 5c | 6c |…

Let the six numbers a₁, a₂, a₃, a₄, a₅, a₆ be in A.P., and a₁ + a₃ = 10. If the mean of these six numbers is 19/2 and their variance is σ²,…

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…

If the variance of the frequency distribution xᵢ 2 3 4 5 6 7 8 fᵢ 3 6 16 α 9 5 6 is 3, then α is equal to:

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…

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…

Let 9 = x₁ < x₂ < … < x₇ be in an A.P. with common difference d. If the standard deviation of x₁, x₂, …, x₇ is 4 and the mean is x, then x…

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 σ²…

If the mean and variance of the frequency distribution | xᵢ | 2 | 4 | 6 | 8 | 10 | 12 | 14 | 16 | |---|---|---|---|---|---|---|---|---| |…

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:

Let m be the mean and σ be the standard deviation of the distribution: | xᵢ | 0 | 1 | 2 | 3 | 4 | 5 | |---|---|---|---|---|---|---| | fᵢ |…

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

Let the positive numbers a₁, a₂, a₃, a₄, and a₅ be in a G.P. Let their mean and variance be 31/10 and m/n, respectively, where m and n are…

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…

The mean and standard deviation of 10 observations are 20 and 8 respectively. Later on, it was observed that one observation was recorded…