Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
BITSAT 2024Paper 1
Exam
BITSAT
Year
2024
Paper
Paper 1
Subject
Mathematics
Chapter
Statistics

BITSAT 2024 · Paper 1 · Mathematics · Statistics

The mean of n items is X. If the first item is increased by 1 ,...

The mean of n items is X. If the first item is increased by 1 , second by 2 and so on, the new mean is :

Options

  1. AXˉ+x2\bar{X}+\frac{x}{2}
  2. BXˉ+x\bar{X}+x
  3. CX‾+n+12\overline{\mathrm{X}}+\frac{\mathrm{n}+1}{2}
  4. DNone of these

Correct answer

C. X‾+n+12\overline{\mathrm{X}}+\frac{\mathrm{n}+1}{2}

Step-by-step solution

Let the items be a1,a2,……..,an\mathrm{a}_1, \mathrm{a}_2, \ldots \ldots.., \mathrm{a}_{\mathrm{n}} then Xˉ=a1+a2+…….+ann\bar{X}=\frac{a_1+a_2+\ldots \ldots.+a_n}{n} Now, according to the given condition: Xˉ=(a1+1)+(a2+2)+………+(an+n)n=X‾+1+2+3+………+nn=Xˉ+n(n+1)2n\bar{X}=\frac{\left(a_1+1\right)+\left(a_2+2\right)+\ldots \ldots \ldots+\left(a_n+n\right)}{n}=\overline{\mathrm{X}}+\frac{1+2+3+\ldots \ldots \ldots+n}{n}=\bar{X}+\frac{n(n+1)}{2 n} (using sum of n natural nos.) =X‾+n+12=\overline{\mathrm{X}}+\frac{\mathrm{n}+1}{2}.
Practice Statistics on Quantrex Academy →

More from Statistics

If the variance of the data 2,3,5,8,12 is σ^2 and the mean deviation from the median for… BITSAT 2024The variance of 20 observations is 5. If each observation is multiplied by 2 , then the… BITSAT 2024If the function f(x) , defined below, is continuous on the interval [0,8] , then f(x)=\… BITSAT 2024The standard deviation of 5 scores 1,2,3,4,5 is a . The value of ' a ' is BITSAT 2023Find the mean deviation about the mean for the data 4,7,8,9,10,12,13,17 BITSAT 2023The mean of five observations is 4 and their variance is 5.2 . If three of these… BITSAT 2022The arithmetic mean of a set of observation is ¯ X . If each observation is divided by α… BITSAT 2018If the variance of the observations x _ 1 , x _ 2 , … … , x _ n is σ ^ 2 , then the… BITSAT 2017Coefficient of variation of two distributions are 50 and 60 and their arithmetic means… BITSAT 2017The arithmetic mean of the data 0,1,2, … …, n with frequencies 1, ^ 4 C_ 1 ^ 4 C_ 2… BITSAT 2015The mean square deviation of a set of n observation x_ 1 , x_ 2^ 2 , … x_ n about a point… BITSAT 2015IfM. D. is 12, the value of S.D. will be BITSAT 2014If the value of mode and mean is 60 and 66 respectively, then the value of median is BITSAT 2013Find the variance of the data given below BITSAT 2013If sample A contains 100 observations 101,102, … 200 and sample B contains 100 obsections… BITSAT 2012Find the value of _ x arrow 0 (1+x^2) - 1-x^2 x^2 BITSAT 2010 Full Statistics list Statistics JEE Maths PYQsJEE Mathematics PYQs All BITSAT PYQs