Dispersion (Variance and Standard Deviation) - Practice Questions & MCQ

All the students of a class performed poorly in Mathematics. The teacher decided to give grace marks of 10 to each of the students. Which of the following statistical measures will not change even after the grace marks are given?

Let   be n observations, and let   be their arithmetic mean and  be their variance.

Statement 1: Variance of .

Statement 2: Arithmetic mean of .

The mean of the numbers and the variance is Then which one of the following gives possible values of ?

The sum of 100 observations and the sum of their squares are 400 and 2475, respectively.  Later on, three observations, 3, 4 and 5, were found to be incorrect.  If the incorrect observations are omitted, then the variance of the remaining observations is :

Let $\mathrm{a}_1, \mathrm{a}_2, \ldots \mathrm{a}_{10}$ be 10 observations such that $\sum_{\mathrm{k}=1}^{10} \mathrm{a}_{\mathrm{k}}=50$ and $\sum_{\forall \mathrm{k}<\mathrm{j}} \mathrm{a}_{\mathrm{k}} \cdot \mathrm{a}_{\mathrm{j}}=1100$. Then the standard deviation of $\mathrm{a}_1, \mathrm{a}_2, \ldots, \mathrm{a}_{10}$ is equal to: