Q74.Let X = {11, 12, 13, … . , 40, 41} and Y = {61, 62, 63, . . . , 90, 91} be the two sets of observations. If x and y ¯are their respective means and σ2 is the variance of all the observations in X ∪Y, then x + y −σ2 is equal to ________
What This Question Tests
This problem requires calculating the means of two given sets, then finding the variance of their union. It tests the ability to apply definitions of mean and variance, especially for combined data sets.
Concepts Tested
Formulas Used
Mean = Σx / n
Variance σ² = (Σx² / n) - (mean)²
Combined mean/variance formulas
📚 NCERT Sections This Tests
13.2 — Obtain The Binding Energy Of The Nuclei 5626Fe And 20983 Bi In Units Of
Physics Class 12 · Chapter 13
13.2 Obtain the binding energy of the nuclei 5626Fe and 20983 Bi in units of MeV from the following data: m ( 5626Fe ) = 55.934939 u m ( 20983 Bi ) = 208.980388 u
13.5 — The Q Value Of A Nuclear Reaction A + B ® C + D Is Defined By
Physics Class 12 · Chapter 13
13.5 The Q value of a nuclear reaction A + b ® C + d is defined by Q = [ mA + mb – mC – md]c2 where the masses refer to the respective nuclei. Determine from the given data the Q-value of the following reactions and state whether the reactions are exothermic or endothermic. (i) 11 H+13 H →12 H+12 H (ii) 126 C+126 C →1020 Ne+ 24 He Atomic masses are given to be m ( 12 H ) = 2.014102 u m ( 13 H) = 3.016049 u m ( 126 C ) = 12.000000 u m ( 1020 Ne ) = 19.992439 u
2.1 — Two Charges 5 × 10–8 C And –3 × 10–8 C Are Located 16 Cm Apart. At
Physics Class 11 · Chapter 2
2.1 Two charges 5 × 10–8 C and –3 × 10–8 C are located 16 cm apart. At what point(s) on the line joining the two charges is the electric potential zero? Take the potential at infinity to be zero.
📋 Question Details
- Chapter
- Statistics
- Topic
- Mean and variance of combined data
- Year
- 2023
- Shift
- 29 Jan Shift 2
- Q Number
- Q74
- Type
- Numerical
- NCERT Ref
- Class 11 Mathematics Ch 15: Statistics
More from this Chapter
Q98.The average marks of boys in a class is 52 and that of girls is 42 . The average marks of boys and girls combined is 50 . The percentage of boys in the class is (1) 40 (2) 20 (3) 80 (4) 60
Q84.The mean of the numbers a, b, 8, 5, 10 is 6 and the variance is 6.80. Then which one of the following gives possible values of a and b ? (1) a = 0, b = 7 (2) a = 5, b = 2 (3) a = 1, b = 6 (4) a = 3, b = 4 JEE Main 2008 JEE Main Previous Year Paper
Q71.If the mean deviation of number 1, 1 + d, 1 + 2d, … . , 1 + 100d from their mean is 255 , then the d is equal to (1) 10.0 (2) 20.0 (3) 10.1 (4) 20.2
Q72.Statement-1 : The variance of first n even natural numbers is n2−14 Statement-2 : The sum of first n natural numbers is n(n+1) 2 and the sum of squares of first n natural numbers is n(n+1)(2n+1)6 (1) Statement-1 is true, Statement-2 is true; (2) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-2 is not a correct explanation for Statement-1 Statement-1 (3) Statement-1 is true, Statement-2 is false (4) Statement-1 is false, Statement-2 is true