Let the mean and variance of four numbers $3,7, x$ and $y(x>y)$ be 5 and 10 respectively. Then the mean of four numbers $...

An online exam is attempted by 50 candidates out of which 20 are boys. The average marks obtained by boys is 12 with a variance...

The mean and standard deviation of 20 observations were calculated as 10 and 2.5 respectively. It was found that by mistake one data value was...

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...