Mean,median,mode

Question

Do you weigh six packages and find out the weights to be 28 22 52 25 49 and 46 ounces. If you include a package that weighs 142 ounces , which will increase more the median order the mean?

A. The median and the mean will stay the same

B. median and the mean are affected the same amount

C. The median increases more

D. The mean increases more

Answer 1

It's always best to sort your data set before working to determine median values, so let's sort our six package weights from smallest to largest:

22 25 28 46 49 52

We know the mean of the set is the average of them, or (22+25+28+46+49+52) / 6 = 37

Similarly, we know the median is the middle number, which in an even set is the sum of the middle two numbers (bold above): (28 + 46) / 2 = 37

Our next step is to understand how adding 142 to the set affects the mean and median, so let's take a look at our new set:

22 25 28 46 49 52 142

We immediately see that the median is now 46, which has increased by 9 (46 - 37)

What about our mean? (22 + 25 + 28 + 46 + 49 + 52 + 142) / 7 = 52. This is an increase of 15.

With this information we can conclude that: the mean increases more

This problem teaches us something very important about statistics: outliers have a big impact on the mean, which usually makes the median a far better representation of a large set of data!