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Suggested answer to exercise: Summarising Data, 6

Question 6: Which Honourable Member is correct, if any, and why?

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Suggested answer

Mr Lloyd is correct that the mean is not the same as the median
but his definition of the median is wrong.
It is the middle number when the numbers are arranged in ascending order and
not the difference between the minimum and maximum values.
So using his first example (2, 2, 5, 6, 7), the median here would be 5 and not 3.5
as asserted.
He is correct that altering the extreme values will not change the median
but his argument is confused.

Mr Carrington is correct that the median is not the mid-point between the
first number and the last but is wrong in his definition.
His definition appears to be referring to the mode of a distribution, i.e.
the category which has the highest frequency, although his explanation
is not very clear.
His definition of the average is wrong (the sample multiplied by the number of items).
He is wrong in stating that the median will change if the number at the bottom
of the scale changes.
This will not change the median but will alter the mean.

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Last updated: 27 July, 2009.

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