Question

What happens to the mean, median and mode for the data shown if the outlier is eliminated?

14 , 15 , 22 , 15 , 44 , 16 , 17 , 13

Answer 1

step 1: calculate the mean. calculate the mode. calculate the median.

step 2: delete the outlier

step 3: repeat step 1

step 4: ???

Step 5: PROFIT!

Answer 2

What is the outlier?

Answer 3

Which one do you think?

Answer 4

idk 22 or 44?

Answer 5

44.

"In statistics, an outlier is an observation that is numerically distant from the rest of the data."

Answer 6

ohhh ok :D

Answer 7

With outlier
Mean : 19.5
Median: 15.5
Mode: 15

Answer 8

am i right?

Answer 9

The median is not really affected by the outlier, but the mean is, and mode can potentially be, if the outlier itself is the largest value.,

Answer 10

For instance, let us suppose that the outlier was a really large value. Including the outlier in our calculations to get the mean, we find that the mean is very large

Answer 11

To really find out what happens, what you should do is first calculate the mean, median and mode WITH the outlier, and then calculate those 3 statistical values again WITHOUT the outlier.

Observe for differences.

Answer 12

i calculated with the outlier am i right?
Mean : 19.5
Median: 15.5
Mode: 15

Answer 13

QRA, the mode won't be affected. The median would be affected. Also the mean.

Answer 14

First of all, have you identified which value is the outlier?

Answer 15

yes 44

Answer 16

Actually @slaaibak, is not the mode that highest value (though that is one definition), or one of the peaks on the visual display? If it is the highest value, then the mode will be affected

Answer 17

The mode is affected in that if the outlier is included, then the mode is the outlier.

Answer 18

The mode is the value that occurs the most.

Answer 19

Let me check my statistics textbook. :D

Answer 20

am i right???
Mean : 19.5
Median: 15.5
Mode: 15

Answer 21

That is with the outlier

Answer 22

A mode: a hump or local high point in the shape of the distribution of a variable.

Answer 23

yes Gabylovesyou you are correct, those the correct values if you include the outlier

Answer 24

thank you @jim_thompson5910

Answer 25

We could assume that this set of numbers is for a quantitative variable, and draw out a histogram and see that 44 in fact, is the mode.

Answer 26

yw

Answer 27

Sorry I went on a tangent there.

Answer 28

The other posters have gone over the basics and the answers. I'm just posting this to tidy everything up


With Outlier

mean = 19.5
median = 15.5
mode = 15


Without Outlier

mean = 16
median = 15
mode = 15


So the mean and median are affected/changed when the outlier is eliminated.

Answer 29

@Gabylovesyou, what is the definition of the mode that you use in class or for this question?

Answer 30

mode = most! in this example the mode is 15

Answer 31

the mode is the most frequent value, I'm not sure which definition you're thinking of QRAwarrior

Answer 32

Oh ok I understand what I did wrong. The mode is the highest peak because it is the value that has been recorded the most.

Answer 33

Sorry about that.

Answer 34

QRA you're taking the mode in a different context here.. you're thinking about probabilities assigned etc. Thats with probability distributions, where the max is the point that is most likely to occur

Answer 35

for example: 15,15,15,15,15,15,16,24,25

15 would be the highest bar

Answer 36

@slaaibak I think it was a misunderstanding, see above post

Answer 37

Shot, no problem

Answer 38

its ok @QRAwarrior

Answer 39

Im going to give u a medal for trying :D