Question

If one number in a data set is changed, will this affect the meadian of the given collection of data? ​

Answer 1

Answer:

If we add or remove a data point from the set, it can effect the median, but it may not. In the set 1 , 2 , 3 , 4 , 4 , 6 , 6 1,\ 2,\ 3,\ 4,\ 4,\ 6,\ 6 1, 2, 3, 4, 4, 6, 6, the median is 4. The same will be true for adding in a new value to the data set.

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Answer 2

Given :       One number in a data set is changed

To  Find : will this affect the median of the given collection of data

Solution:

Median =  middle term in Data

If   One number in a data set is changed then  Median May change or may not change

Data can be interpreted as  

Lower Quartile Median Upper Quartile

if Data change in lower Quartile remains in lower Quartile then no impact on Median

if Data change in Upper Quartile remains in upper Quartile then no impact on Median

But if Data Changes from Lower to upper  or upper to lower then it can impact the median

Examples

1  2 3 3 4 6 7 7  8 9 9

Median is 6

if any of 1  2 3 3 4  is changed to any number  ≤ 6 then no change on median

if any of 7 7  8 9 9  is changed to any number  ≥ 6 then no change on median

if 6 is changed to any other number median will be changed

if any of 1  2 3 3 4  is changed to any number > 6 then median will change  

if any of  7 7  8 9 9   is changed to any number < 6 then median will change

If one number in a data set is changed, will this affect the median of the given collection of data may change or may not change

Another example :

1  2 3 3 4 5 5 5 6 7 7 8 9

No impact on median on changing any one number in this data set

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