Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main 20149 AprilOnline
Exam
JEE Main
Year
2014
Date
9 April
Mode
Online
Subject
Mathematics
Chapter
Statistics

JEE Main 2014 · 9 April · Online · Mathematics · Statistics

In a set of 2n distinct observations, each of the observation below...

In a set of 2n2n distinct observations, each of the observation below the median of all the observations is increased by 55 and each of the remaining observations is decreased by 33. Then, the mean of the new set of observations :

Options

  1. AIncreases by 22 .
  2. BIncreases by 11 .
  3. CDecreases by 22 .
  4. DDecreases by 11 .

Correct answer

B. Increases by 11 .

Step-by-step solution

New mean=(nΣxi+5n)+(nΣyi−3n)2n= \dfrac{\left(\text{n}Σ{x}_{i} + \text{5n}\right) + \left(\text{n}Σ{y}_{i} - \text{3n}\right)}{\text{2n}}

={nΣxi+nΣyi2n}+2n2n= \left\{\dfrac{\text{n}Σ{x}_{i} + \text{n}Σ{y}_{i}}{\text{2n}}\right\} + \dfrac{\text{2n}}{\text{2n}}

=old mean +2n2n+ \dfrac{\text{2n}}{\text{2n}}

=old mean+1+ 1
Practice Statistics on Quantrex Academy →

More from Statistics

Consider a data consisting of 10 observations x_1, x_2, …, x_ 10 , whose mean is 5 and… JEE Advanced 2026A set of four observations has mean 1 and variance 13 . Another set of six observations… JEE Main 2026Let the mean and the variance of seven observations 2, 4, α, 8, β, 12, 14 , α < β , be 8… JEE Main 2026A data consists of 20 observations x_1, x_2, …, x_ 20 . If ∑_ i=1 ^ 20 (x_i + 5)^2 = 2500… JEE Main 2026A variable X takes values 0, 0, 2, 6, 12, 20, …, n(n-1) with frequencies ^nC_0, ^nC_1… JEE Main 2026The mean deviation about the mean for the data x_i 5 7 9 10 12 15 f_i 8 6 2 2 2 6 is… JEE Main 2026For 10 observations x_1, x_2, …, x_ 10 , if ∑_ i=1 ^ 10 (x_i+2)^2=180 and ∑_ i=1 ^ 10… JEE Main 2026Suppose that the mean and median of the non-negative numbers 21, 8, 17, a, 51, 103, b… JEE Main 2026The mean and variance of n observations are 8 and 16 , respectively. If the sum of the… JEE Main 2026If the mean of the data Class 5-10 10-15 15-20 20-25 25-30 30-35 Frequency 2 k 28 54 k+1… JEE Main 2026The mean and variance of 10 observations are 9 and 34.2, respectively. If 8 of these… JEE Main 2026Let X=\ x ∈ ~N: 1 ≤ x ≤ 19\ and for some a, b ∈ ℝ, Y=\ a x+b: x ∈ X\ . If the mean and… JEE Main 2026The mean and variance of a data of 10 observations are 10 and 2, respectively. If an… JEE Main 2026If the mean and the variance of the data Class 4-8 8-12 12-16 16-20 Frequency 3 λ 4 7 are… JEE Main 2026Let the mean and variance of 8 numbers -10,-7,-1, x, y, 9,2,16 be (7)/(2) and (293)/(4)… JEE Main 2026If the mean deviation about the median of the numbers k, 2 k, 3 k, …. ., 1000 k is 500… JEE Main 2026 Full Statistics list Statistics JEE Maths PYQsJEE Mathematics PYQs All JEE Main PYQs