1
JEE Main 2021 (Online) 17th March Evening Shift
Numerical
+4
-1
Consider a set of 3n numbers having variance 4. In this set, the mean of first 2n numbers is 6 and the mean of the remaining n numbers is 3. A new set is constructed by adding 1 into each of first 2n numbers, and subtracting 1 from each of the remaining n numbers. If the variance of the new set is k, then 9k is equal to __________.
2
JEE Main 2021 (Online) 16th March Evening Shift
Numerical
+4
-1
Consider the statistics of two sets of observations as follows :

Size Mean Variance
Observation I 10 2 2
Observation II n 3 1

If the variance of the combined set of these two observations is $${{17} \over 9}$$, then the value of n is equal to ___________.
3
JEE Main 2021 (Online) 26th February Evening Shift
Numerical
+4
-1
Let X1, X2, ......., X18 be eighteen observations such
that $$\sum\limits_{i = 1}^{18} {({X_i} - } \alpha ) = 36$$ and $$\sum\limits_{i = 1}^{18} {({X_i} - } \beta {)^2} = 90$$, where $$\alpha$$ and $$\beta$$ are distinct real numbers. If the standard deviation of these observations is 1, then the value of | $$\alpha$$ $$-$$ $$\beta$$ | is ____________.
4
JEE Main 2021 (Online) 24th February Evening Shift
Numerical
+4
-1
If the variance of 10 natural numbers 1, 1, 1, ....., 1, k is less than 10, then the maximum possible value of k is ________.