Question

When an observation that is much larger than the rest of the data is added to a data​ set, the value of the median will increase substantially. true or false?

Answer 1

False.  However the mean will increase substantially.

Answer 2

You can use the fact that median is not affected by the value of the data unless its the middle value of the data.

The given statement is False.

When does a median changes of a given data set?

Median is not a representative of "value" of the data set. It just represents what is the value for which in the data set (sorted ascending or descending) half of the data set values will lie on its one side, and other half will lie on its other side.

Suppose that you've got the data set as 3,5,2,7,5,3,2,6,8

Now sorting it (arranging it in either increasing or decreasing way),

2,2,3,3,5,5,6,7,8

There are total 9 observations. The median is the 5th observation as there are 4 observations to its left and 4 observation to its right.

Since in the given condition, a large number, larger than the rest of the data is added, thus, in sorted data, it will be lying either on the leftmost or the rightmost position, and will only allow median to shift a little bit(depending on other values in the mid of the data set) just because of "count increment" of the size of the data set and not because of the value of the data added.

Thus,

The given statement is False.

Learn more about median here:

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