Question

The price of a cheeseburger is listed for 10 different restaurants. Which measure would give the most accurate representation of the average price of a hamburger?
($2.50,2.00,3.00,8.50,2.75,3.00,2.50,3.50,2.75,1.00)
1. mode
2. median
3. range

Answer 1

Which do you think it is?

Answer 2

I think all of them cannot be the answer.

Answer 3

One of them is the correct answer.

Answer 4

Because we have too many modes

Answer 5

And for median, we have 8.50. So I think median couldn't be the answer, too

Answer 6

For range, it seems odd because we get 7 something

Answer 7

$8.50 is expensive for a hamburger. It is an outlier. But it is still part of our data set so we can't just get rid of it.

Answer 8

Yeah.

Answer 9

Range doesn't really tell us anything about the values of our data. It just tells us how far apart items in our data are.

Answer 10

Oh that sounds correct. So we can get rid of Range

Answer 11

Yup.

Answer 12

Then we have mode and median

Answer 13

What about mode and median?

Answer 14

What does mode tell us about our data?

Answer 15

It tells us which data is most frequent

Answer 16

But we have two modes.

Answer 17

Do our modes take into account all of the prices in our data set?

Answer 18

Nope (?)

Answer 19

Then the mode can't very well give us an average representation of ALL of our data

Answer 20

oh yeah. so the answer is median? But I want to make sure that whether the median shows us the average price of a hamburger

Answer 21

Since we have an outlier, I wonder it could show the average price of a hamburger or not

Answer 22

This is nasty question!

Answer 23

It will. The outlier will affect our data, but if you gave someone the average price of a hamburger in that city without the individual prices it would be deceptive because all of the data points don't lie near the median.

Answer 24

In a perfect situation (in a "nice" data set), all of the data lies more or less around the median. However, in some situations, an outlier will pull the median one way or another.

Answer 25

Oh so for mode, since we have two modes, mode can't show us the average price. For range, it just shows us how far they are. And for median, it shows us the average price?

Answer 26

Median is synonymous with the average of a set of data.

Answer 27

Even if we have one mode, the mode only takes into consideration the items that occur more than once.

Answer 28

So it isn't very helpful for determining something like the average

Answer 29

Oh. the mode only takes into consideration the items that occur more than once. That is clear. Thank you.
Umm I have the farther question. sorry. Isn't the mean the synonym for average?
Does mean can be the answer, too? Because I chose "mean", and I got wrong.

Answer 30

Oh goodness. I don't know why I was mixing up median and mean

Answer 31

However, the median would still be the correct answer

Answer 32

Could you explain why?

Answer 33

Median is the one you get when you add all the data and dived them up. right? Median is just the middle number?

Answer 34

It would be a little more accurate to say "Which - of the available- measures would give the most accurate representation of the average price of a hamburger?"

Answer 35

Mean is when you add them up and divide them. Median is the middle value of our set

Answer 36

Oh yeah. But I am still confused because of the mean. Could you explain why median is the answer for this question?

Answer 37

The median of a set gives the most correct average of a set when the values in the set are uniformly distributed - so that there aren't a lot of outliers.