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

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

Question

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

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

johnweldon1993 · Answer

Well which number here is the outlier?

anonymous · Answer

44

johnweldon1993 · Answer

Well first lets check to make sure that is the ONLY one

First start by finding the median

13, 14, 15, 15, 16, 17, 22, 44

Median looks to be the average of 16 + 15 = 15.5

Now what is the upper quartile (Q3)? It is the median of the upper half...or 19.5

And the lower quartile? (Q1)? It is the median of the lower half...or 14.5

Now we need to find the IQR (Inter-Quartile Range) Q3 - Q1 = 19.5 - 14.5 = 5

So,,,To find an outlier of a set of data...you take the Lowest Quartile (Q1) Multiply it by 1.5 and then subtract that IQR (5)

So

14.5 - (1.5 x 5) = 7    so any number lower than 7 will be an outlier

To find the other way...we do Q3 + (1.5 x IQR)

so

19.5 + (1.5 x 5) = 27

So any number greater than 27 is an outlier...

so yes, 44 is the only outlier here..

johnweldon1993 · Answer

If we remove it, the list looks like

13, 14, 15, 15, 16, 17, 22

Now the mew median will be the middle there or 15

The mean will now be the average (13+14+15+15+16+17+22)/2 = 56

And the mode will still be 15 since it is the only number that appears twice

anonymous · Answer

Thank You ! Can You help me with another question ? I don't understand it at all. @johnweldon1993

johnweldon1993 · Answer

Yeah sure, And I'll actually walk you through it this time lol :)

anonymous · Answer

Randall set a personal goal to exercise at least twenty minutes for most of the days during the last two months. He recorded his exercise time each day. Use the box and whisker plot of his data to determine whether he reached his goal. Explain.

johnweldon1993 · Answer

Alright so it is good to be able to point out "key words" in the paragraph.

So since he wants to exercise at least 20 minutes most days of the weeks (doesn't mean he will ALWAYS hit 20 but wants to be at 20 averagely) we will want to find the median of our data

Because the median is the middle, so he went over some days, he went under some days, but when averaged out he went at least (the median)

So here, the median is represented by that line INSIDE the box, we can see it is right at 20 minutes, so this means that yes, he did accomplish his goal