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
=…
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