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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 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 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 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 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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