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?

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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?

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Answer 1 · 2017-06-16T09:10:42

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

Explanation:

The data is completely symmetric as

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

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

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

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

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

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

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

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

= $\frac{10 x + 10 y}{10} = x + y$ $(10x+10y)/10=x+y$

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

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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?

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