# Statistics Examples

Here you will learn some statistics examples for better understanding of statistics concepts.

Example 1 : If mean of the seies $$x_1$$, $$x^2$$, ….. , $$x_n$$ 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

$$\bar{X}$$ = $$(x_1+2) + (x_2+2.2) + (x_3+2.3) + …. + (x_n + 2.n)\over n$$

= $$x_1 + x_2 + …. + x_n\over n$$ + $$2(1+2+3+….+n)\over n$$

= $$\bar{x}$$ + $$2n(n+1)\over 2n$$

= $$\bar{x}$$ + n + 1.

Example 2 : 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 = 60%

Example 3 : 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 $$\implies$$ $$x_1 + x_2 + 1 + 2 + 6\over 5$$ = 4 $$\implies$$ $$x_1 + x_2$$ = 11     …..(2)

from eq.(1), (2)     $$x_1$$, $$x_2$$ = 4, 7

Practice these given statistics examples to test your knowledge on concepts of statistics.