Question

https://s9.postimg.org/tj2ugch9b/Untitled1.png

I'm not quite sure how to figure this one out.

I know the mean is the arithmetic average of a data set in the median tells us half of the values that fall below and half of the values that fall above; also how to find the mean and median, but I don't know which choice to pick based off of these choices alone.

Answer 1

take 2 examples
scores = {5,6,97,98,99,99,100,100}, what is the mean and median?

scores = {1,1,3,4,5,5,100,100}, what is the mean and median?

Answer 2

What would be the general rule though for a mean being smaller than a median?

@518nad

Answer 3

have u found the median and mean of those 2 data sets

Answer 4

Am finding right now

Answer 5

75.5
98.5

Answer 6

27.375
4.5

Answer 7

Why is it like this?

Answer 8

@518nad

Answer 9

You still here?

Answer 10

Yes

Answer 11

@Seratul

Answer 12

Still here?

Answer 13

I'm here. Ha.

Answer 14

@mathmate

Seems like I'm tagging you again dear.

Answer 15

hint:

when there is a data set that has a few outliers, the mean will be "pulled" towards the outliers

example: if we measure the height of 100 random people, and then a few very tall basketball players walk in, the mean will be shifted up. therefore, the mean will probably be higher than the median

the opposite wold happen if a bunch of very short people walked in

does this make sense?

Answer 16

Yes I'm thinking.

Answer 17

It makes sense, but I want to know why it does that.

What about the mean and median make them so different that one would be small and one would be big based on that data set? It's their properties I'm trying to understand, although I know what a mean and median is. I want to know why all the other choices in the screenshot are wrong.

Answer 18

that's a very good question!

best way to explain it is that: the mean is based on the value of each number, while the median is based on the position of each number.

let's say we have a data set:

1,2,3,4,5

which has a median of 3 and a mean of 3

Answer 19

we can add 10 to the set, which makes the mean 4.167 and the median 3.5

Answer 20

if we add 100 to the set instead of 10, the mean is 19.167 and the median is still 3.5

Answer 21

since the median is only affected by position, it tends to change less than the mean

Answer 22

I hope that makes it a little clearer

Answer 23

To give you context,
@518nad 's examples:
`scores = {5,6,97,98,99,99,100,100}, what is the mean and median?`
`scores = {1,1,3,4,5,5,100,100}, what is the mean and median?`
The first one is for an easy exam, almost everyone got full marks. The two low marks are probably those who didn't go to class, or those who got direct answers from math sites.
The second example is a typical VERY difficult exam. The two who got 100 are either geniuses or they studied day and night for the exam.
Now examine the marks of each example, compare with the mean and median for each example that you calculated. See if you can visualize something out of them.

Answer 24

@mathmate

I haven't been able to see anything, yet.

Answer 25

I'm still looking.

Answer 26

distribution of the two exams