Question

3. The ages of the first 14 customers in line to purchase movie tickets are shown below.
27 18 46 57 22 24 29 34 18 19 22 31 31 51
(a) What are the lower and upper fences of the data set? Show your work.
(b) Draw the modified box-and-whisker plot for the data set.

Answer 1

for b are they saying that I have to find and plot the 5 summary data?

Answer 2

Why not go "whole hog" and find the entire 5-number summary?

Yes, you do need to find and plot the 5-number summary.

Arrange the data in ascending order and find the median.

Answer 3

would the lower be 18 and the upper fence be 57?

Answer 4

one moment please as I find b

Answer 5

Freemap: I need to see your work. This question specifically asks you to show all work.

Answer 6

okay hold please

Answer 7

First and foremost: Arrange your data in ascending order.
Next, find the median.

The data now appear as:


The median is:

Answer 8

I'm sorry I had to do it over because i messed up the numbers sorry. please hold

Answer 9

18,18,19,22,22,24,27,29,31,31,34,46,51,57 okay since we have an even number theres two in the middle 27+29=46, 46/2=23

Answer 10

median is 23

Answer 11

Yes. That's the first number of your 5-number summary.
Which are the next numbers you must find or calculate?

Answer 12

mean is 214.5 I added all the numbers and got 429/2=214.5

Answer 13

Lower Q is 20.5, 19, 22 so 19+22=41/2=20.5
Upper Q is 40, 34, 46 so 34+46=80/2=40

Answer 14

min is 18 and the max is 57

Answer 15

I think I got everything

Answer 16

I'm not checking your results, but you sound confident. Note that the mean is not part of the 5-number summary, but calculating it is fine. Extra credit for you today.

Answer 17

okay thanks so much for all your help I know how to make the whisker box

Answer 18

There are 10 numbers in your data set. The median is the average of 27 and 29.
How many numbers are on either side of your median? If that number is odd, then you simply choose the number in the middle. Would you mind trying this?

Answer 19

6 numbers are on the side of the median it is even

Answer 20

18,18,19,22,22,24,27,29,31,31,34,46,51,57 okay since we have an even number theres two in the middle 27+29=46, 46/2=23

sorry, I'll have to ask you to check your calculations. What is the sum of 27 and 29? It's not 46.

Answer 21

I count 14 numbers in 18,18,19,22,22,24,27,29,31,31,34,46,51,57.

Answer 22

True, the median is between 27 and 29, but is not 23.

Answer 23

(27+29)/2=?

Answer 24

56/2=28

Answer 25

Thanks for catching that

Answer 26

Yes. How many numbers are on the left of 28 ? On the right of 28?

Answer 27

do you mean 29 if so, 6

Answer 28

But your median is (27+29)/2, or ... ?

Answer 29

I thought it was 28

Answer 30

I see now

Answer 31

It is. So, how many numbers are to the left of 28?

Answer 32

6 number would be on the right still because 27 and 29 become 1 to make 28 ?

Answer 33

there are 14 data points. The median is 28. Half of these 14 data points lie to the left of 28. How many?
5, 6, 7 or 8?

Answer 34

Note that '28' isn't actually in your data set. We calculated it: (27+29)/2=28.

Answer 35

4

Answer 36

I count 7 data points to the left of 28 and 7 to the right.
Agree or disagree? Why?

Answer 37

I finally get it now i think, so half of 14 is 7, we have to half's so 7 for one and 7 for another make 14. I agree

Answer 38

Since the number of data points to the left of 28 is 7, your Q1 (first quartile) is the middle data point. What is that point?

I count 14 numbers in 18,18,19,22,22,24,27,29,31,31,34,46,51,57
To the left of median 28, I count 7 numbers: 18,18,19,22,22,24,27

What is the number that appears in the middle of this subset?

Answer 39

22

Answer 40

Right. That's your Q1. What is your Q3? Explain how you'll find it.

Answer 41

So basically I will count how many number there are and half it. and find out the Q1 for the lower half and the Q3 for the upper half. Q1 is 22 and Q3 is 34

Answer 42

Yes, 34.

What is your minimum? your maximum?

Answer 43

min 18 and max 57

Answer 44

What is your five number summary?

Answer 45

so median is 28
lower q is 22
upper q is 34
min 18
max 57

Answer 46

Great. Any questions about the process of finding this 5-number summary, or about finding medians?

Answer 47

I learned the process long thanks for you time this is the same as if you were doing it the other way?

Answer 48

Not sure what you're asking, sorry.
Every other process would be roughly similar to the one we've used.

Answer 49

Thanks again

Answer 50

My pleasure. Good luck!

Answer 51

(a) What are the lower and upper fences of the data set? Show your work.
(b) Draw the modified box-and-whisker plot for the data set.

Looks as tho' you still have a bit more work to do to complete this problem.

What is a "lower fence?"

Answer 52

Please see the following:

http://www.purplemath.com/modules/boxwhisk3.htm