Question

What are the mean, median, mode, and range of the data set given the altitude of lakes in feet:

–12, –9, –14, –39, –49, –49, –18, and –43?

A. mean = –28.5, median = –29.1, mode = –49, range = 40
B. mean = –29.1, median = –49, mode = –28.5, range = 41
C. mean = –49, median = –29.1, mode = –28.5, range = 41
D. mean = –29.1, median = –28.5, mode = –49, range = 40

Answer 1

mean = average

In this case:

mean = [ - 12 + ( - 9 ) + ( - 14 ) + ( - 39 ) + ( - 49 ) + ( - 49 ) + ( - 18 ) + ( - 43 ) ] / 8 =

( - 12 - 9 - 14 - 39 - 49 - 49 - 18 - 43 ) / 8 = - 233 / 8 = - 29.125

The median is the "middle" value in the list of numbers.

When numbers are sorted from lowest to highest, the median is the mean value in the list of numbers.

If we find middle pair of numbers, then find the value of median is halfway between them.

In this case:

- 49 , - 49 , - 43 , - 39 , - 18 , - 14 , - 12 , - 9

median = [ - 39 + ( - 18 ) ] / 2 = ( - 39 - 18 ) / 2 = - 57 / 2 = - 28.5

The mode is the value that occurs most often.

In this case:

mode = - 49

because appeared 2 times

The range is the difference between the lowest and highest values.

In this case:

range = - 9 - ( - 49 ) = - 9 + 49 = 40

So answer is D