Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main 201219 MayOnline
Exam
JEE Main
Year
2012
Date
19 May
Mode
Online
Subject
Mathematics
Chapter
Statistics

JEE Main 2012 · 19 May · Online · Mathematics · Statistics

The median of 100 observations grouped in classes of equal width is...

The median of 100 observations grouped in classes of equal width is 25 . If the median class interval is 20-30 and the number of observations less than 20 is 45 , then the frequency of median class is

Options

  1. A10
  2. B20
  3. C15
  4. D12

Correct answer

A. 10

Step-by-step solution

Median is given as M=l+N2−Ff×\frac{\frac{N}{2}-F}{f} \timesC where l=l= lower limit of the median - class f=f= frequency of the median class N=N= total frequency F=F= cumulative frequency of the class just before the median class C=C= length of median class Now, given, M=25,N=100,F=45M=25, N=100, F=45, C=20−30=10,l=20C=20-30=10, l=20. ∴\therefore By using formula, we have25=20+50−45f×1025−20=50f⇒5=50f\Rightarrowf=10\begin{aligned}& 25=20+\frac{50-45}{f} \times10 \\ & 25-20=\frac{50}{f} \Rightarrow5=\frac{50}{f} \Rightarrowf=10 \end{aligned}
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