The mean and variance of seven observations are 8 and 16, respectively. If 5 of the observations are 2, 4, 10, 12, 14, then the...

5 students of a class have an average height 150 cm and variance $18 \mathrm{~cm}^2$. A new student, whose height is 156 cm , joined...

Consider the following frequency distribution

Let $X_1, X_2, \ldots \ldots X_{18}$ be eighteen observations such that $\sum_{i=1}^{18}\left(x_i-\alpha\right)=36$ and $\sum_{i=1}^{18}\left(x_i-\beta\right)^2=90$, where $\alpha$ and $\beta$ are distinct real numbers. If the standard...

A student scores the following marks in five tests : 45, 54, 41, 57, 43. His score is not known for the sixth test. If...

the first of the two samples in a group has 100 items with mean 15 and standard deviation 3 . If the whole group has...

If the mean and variance of the following data :
$6,10,7,13, a, 12, b, 12$ are 9 and $\frac{37}{4}$ respectively, then $(a-b)^2$ is equal...

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...

The mean of 6 distinct observations is 6.5 and their variance is 10.25. If 4 out of 6 observations are 2, 4, 5 and 7,...

Let in a series of $2 n$ observations, half of them are equal to a and remaining half are equal to .a. Also by adding...