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?

1 Answer
Shwetank Mauria
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+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#.

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