Question

For which data set is the mean most likely to be misleading
5, 6, 6, 7, 8, 8, 9, 9, 9, 9

2, 5, 6, 7, 9, 8, 9, 9,10,10

5, 5, 5, 5, 5, 5, 5, 5, 5, 5

2, 3, 4, 5, 5, 5, 5, 8,27, 45

Answer 1

Mean is what most people think of as the average... like if you had 3, 4, and 5, the average is (3 + 4 + 5)/3 = 4.

Mean is misleading when you have a few points really far from the mean.

Imagine a set like 0, 0, 100, 100. Its mean is 50, but that gives you no real idea that the points are all 0s and 100s.

Answer 2

So, just by looking, no calculating, the first three sets are pretty evenly spread around some middle point... the first is probably around 7 or 8, the second might be 6 or 7, and the third is obviously a mean of 5 since all elements are 5.

Answer 3

The last set adds up to 109, and there are 10 numbers, so the mean is 10.9. However, notice that all but two of the numbers are below 10... it's only those last two outliers that pull the mean up to 10. Without those outliers, the mean would be between 4 and 5.

Answer 4

The existence of those outliers in the 4th set makes the mean misleading, because it makes you think most of the points are around 10, when in reality, most are way below 10.

Answer 5

So the last one?

Answer 6

yes it's the last one... does it make sense why?

For another example, it would be like finding the average age of a kindergarten class with a couple elderly people mixed in... most kids will be 5-6 years old, but the mean might be 12-13 years if the elderly people were really old... their ages would be outliers, and the mean of 12-13 would be misleading since the kids are all 5-6 years old.

Answer 7

It's because there is so many different numbers, but then it's goes from 8 to 27.

Answer 8

yes, all the low numbers are grouped together, but then those last two are way up there by comparison.

Answer 9

OK, I got another question it's my last quetsion.