Question

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?

Answer 1

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+2y`

Further mean of `x` and `x+2y`, 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 `(x+x)/2=x`.

Further, mean is `(4xx x+2(x+y)+4xx(x+2y))/10=(4x+2x+2y+4x+8y)/10`

= `(10x+10y)/10=x+y`

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