Central Tendency

• Mean of data sets

Mean or average of a data is given by the formula,

Mean =

Note: 

• • Mean always lies between the highest and lowest observations of the data.
  • It is not necessary that mean is any one of the observations of the data.

1. If the mean of n observations $x_1,x_2,x_3....x_n$ is $\overline{x}$ then $\left(x_1-\overline{x}\right)+\left(x_2-\overline{x}\right)+\left(x_3-\overline{x}\right)+...+\left(x_n-\overline{x}\right)=0$.
2. If the mean of n observations $x_1,x_2,x_3....x_n$ is $\overline{x}$ then the mean of $\left(x_1+p\right), \left(x_2+p\right), \left(x_3+p\right), ..., \left(x_n+p\right)$ is ($\overline{x}$ + p).
3. If the mean of n observations $x_1,x_2,x_3....x_n$ is $\overline{x}$ then the mean of $\left(x_1-p\right), \left(x_2-p\right), \left(x_3-p\right), ..., \left(x_n-p\right)$ is ($\overline{x}$ − p).
4. If the mean of n observations $x_1,x_2,x_3....x_n$ is $\overline{x}$ then the mean of $p{x}_1, p{x}_2, p{x}_3, ..., p{x}_n$ is p$\overline{x}$.
5. If the mean of n observations $x_1,x_2,x_3....x_n$ is $\overline{x}$ then the mean of $\frac{x_1}{p},\frac{ x_2}{p}, \frac{x_3}{p}, ..., \frac{x_n}{p}$ is $\frac{\overline{x}}{p}$.

Example:

The runs scored by a batsman in 6 matches are as follows:

24, 126, 78, 43, 69, 86

What is the average run scored by the batsman?

Solution:

Total number of runs scored = 24 + 126 + 78 + 43 + 69 + 86

   =…