# How do you find the mean, median and mode of x, x, x, x, x+y, x+y, x+2y, x+2y, x+2y, x+2y?

Jun 16, 2017

Mean, median and mode all are $x + y$.

#### Explanation:

The data is completely symmetric as

there are$4$ data points whose value is $x$

there are $2$ data points whose value is $x + y$

and there are again $4$ data points whose value is $x + 2 y$

Further mean of $x$ and $x + 2 y$, only two extreme values, is middle value, which is $x + y$

Hence, data is completely symmetric and there is no skewness.

Hence mean, median and mode all are just $x + y$.

Alternatively, as there are already in ascending order, there are two middle values $x$ and $x$ and hence median is $\frac{x + x}{2} = x$.

Further, mean is $\frac{4 \times x + 2 \left(x + y\right) + 4 \times \left(x + 2 y\right)}{10} = \frac{4 x + 2 x + 2 y + 4 x + 8 y}{10}$

= $\frac{10 x + 10 y}{10} = x + y$

Although for mode we have maximum frequency at two data points $x$ ansd $x + 2 y$ and hence to find mode, we have two modal class. But symmetric nature of data will lead to mode as $x + y$.