Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET202415 May 2024Morning ShiftMathematicsStatisticsActual

The mean of the numbers a, b, 8,5,10 is 6 and the variance is 6 8 . Then which of the following gives possible values of a and b ?

Options

  1. Aa =3, ~b =4
  2. Ba =0, ~b =7
  3. Ca =5, ~b =2
  4. Da =1, ~b =6

Correct answer

A. a =3, ~b =4

Step-by-step solution

aligned & Mean =6 & a+b+8+5+10 5 =6 & a+b=7 & (a-6)=(1-b)...(i) & 6.80= (x_i- x )^2 n & 6.80= (a-6)^2+(b-6)^2+4+1+16 5 aligned aligned & 34=(a-6)^2+(b-6)^2+21 & (a-6)^2+(b-6)^2=13 & (1-b)^2+(b-6)^2=13..[From (i)] & b^2-2 b+1+b^2-12 b+36=13 & 2 b^2-14 b+24=0 & b^2-7 b+12=0 & b=3,4 & b=3 a=4 and & b=4 a=3 aligned

Practice Statistics on Quantrex Academy →

More from Statistics

The variance of a set of 20 observations is 16. If 7 is added to each observation, and then 5 is subtracted from each resulting observation, what will be the new standard deviation 2026If for a distribution of 20 items, (x - 4) = 10 and (x - 4)^2 = 85 then the standard deviation is: 2026Consider the data of scores obtained by students in an examination. If the score of every student is increased by 2 marks, then which of the following statements is TRUE? 2026The mean and standard deviation of 100 items are 50 and 4 , respectively then the sum of all squares of the items is 2026If _ i=1 ^9 (x_i-5 )=9 and _ i=1 ^9 (x_i-5 )^2=45 , then the standard deviation of the nine observations x ₁, x ₂, , x ₉ is 2025Variance of the following continuous frequency distribution is Class Interval 0 – 4 4 – 8 8 – 12 12 – 16 Frequency 1 2 2 1 2025The mean deviation from the median for the following data is x_i 9 3 7 2 5 f_i 1 6 2 8 4 2025The mean deviation about the mean for the following data is Class Interval 0 – 2 2 – 4 4 – 6 6 – 8 8 – 10 Frequency 1 3 4 1 2 2025 Full Statistics list All MHT CET PYQs