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Question 3
Which measures of central tendency get affected if the extreme observations on both the ends of a data arranged in descending order are removed?
(a) Mean and mode
(b) Mean and median
(c) Mode and median
(d) Mean, median and mode

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Solution

(a)
Mean is defined as follows:
Mean=Sum of all the observationsNumber of observations
So, if we remove the extreme values that both sum and the total number of observations will change. Hence, mean will also change.
The mode is that observation which occurs the most. So, if the extreme value of those values which occurs mostly than mode can affect if they are removed.
Median is the mid value. So, if extreme values are removed then the mid value remains same. Hence, the median will not change.

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