# Statistics Questions

## The variance of first 50 even natural numbers is

Solution : $${\sigma^2}$$ = $$\sum(x_i – \bar{x})^2\over n$$ $$\bar{X}$$ = $$\sum x_i\over n$$ = $$2 + 4 + 6 + 8 + ….. + 100\over 50$$ = 51 $${\sigma^2}$$ = $$2^2 + 4^2 + …. + 100^2\over 50$$ – $$51^2$$ = 833 Similar Questions The mean and variance of a random variable X having a …

## The mean and variance of 5 observations of an experiment are 4 and 5.2 respectively. If from these observations three are 1, 2 and 6, then remaining will be

Solution : As given $$\bar{x}$$ = 4, n = 5 and $${\sigma}^2$$ = 5.2. If the remaining observations are $$x_1$$, $$x_2$$ then $${\sigma}^2$$ = $$\sum{(x_i – \bar{x})}^2\over n$$ = 5.2 $$\implies$$ $${(x_1-4)}^2 + {(x_2-4)}^2 + {(1-4)}^2 + {2-4)}^2 + {(6-4)}^2\over 5$$ = 5.2 $$\implies$$ $${(x_1-4)}^2 + {(x_2-4)}^2$$ = 9  …..(1) Also $$\bar{x}$$ = 4 $$\implies$$ …

## A student obtained 75%, 80%, 85% marks in three subjects. If the marks of another subject are added then his average marks can not be less than

Solution : Total marks obtained from three subjects out of 300 = 75 + 80 + 85 = 240 if the marks of another subject is added then the total marks obtained out of 400 is greater than 240 if marks obtained in fourth subject is 0 then minimum average marks = $$240\over 400$$$$\times$$100 = …

## If mean of the series $$x_1$$, $$x^2$$, ….. , $$x_n$$ is $$\bar{x}$$, then the mean of the series $$x_i$$ + 2i, i = 1, 2, ……, n will be

Solution : As given $$\bar{x}$$ = $$x_1 + x_2 + …. + x_n\over n$$ If the mean of the series $$x_i$$ + 2i, i = 1, 2, ….., n be $$\bar{X}$$, then $$\bar{X}$$ = $$(x_1+2) + (x_2+2.2) + (x_3+2.3) + …. + (x_n + 2.n)\over n$$ = $$x_1 + x_2 + …. + x_n\over n$$ …