Question

can someone help me figure out if a box plot is symmetrical or not please im confused

Answer 1

@jim_thompson5910 can you help me please :)

Answer 2

I'll have to see the full problem

Answer 3

ok i have the first half .... i understand it ... The following table shows the number of hours some high school students in two states spend surfing the Internet each week:


State A 35 36 35 34 35 38 36 36 38
State B 24 22 20 50 25 24 65 25 26


Part A: Create a five-number summary and calculate the interquartile range for the two sets of data.

Part B: Are the box plots symmetric? Justify your answer.

Answer 4

Part A: State A Minimum : 34
Quartile 1 : 35
Median : 36 interquartile range: 3
Quartile 3 : 38
Maximum : 38

State B Minimum : 20
Quartile 1 : 23
Median : 25 interquartile range: 17
Quartile 3 : 50
Maximum : 65

Part B:

Answer 5

ok one moment

Answer 6

ok thank you i think they are not symmetric but not sure

Answer 7

focus on the first data set

what is the distance from Q1 to the median?

Answer 8

1 space over

Answer 9

how about from the median to Q3 ?

Answer 10

2 spaces

Answer 11

wait a sec

Answer 12

you have the wrong value for Q3

Answer 13

sort the list for state A
34, 35, 35, 35, 36, 36, 36, 38, 38

highlight the median (in red)
\[\Large 34, 35, 35, 35,\color{\red}{36},36, 36, 38, 38\]
now focus on the values to the right of the median. This list here
36, 36, 38, 38

find the mean of the list `36, 36, 38, 38` to find the value of Q3

Answer 14

mean is 37

Answer 15

you're looking for the median of that subset

but yes, Q3 is 37

Answer 16

State A
Minimum : 34
Quartile 1 : 35
Median : 36
Quartile 3 : 37
Maximum : 38
IQR = 3

notice how Q1 is 1 unit away from the median. Q3 is also 1 unit away from the median
the min is 2 units away from the median. the max is 2 units away from the median

these equal distances on each side of the median prove that the box plot for state A is symmetric

Answer 17

oh ok so because i had the wrong number i was getting it not to be symmetric

Answer 18

so b would not be symmetric because of the big gap between 25 and 50

Answer 19

@jim_thompson5910 does that mean that my state b is wrong too

Answer 20

B is definitely not symmetric

this image visually confirms it

Answer 21

I made a typo, for state A the IQR should be 2

Answer 22

State B
Minimum : 20
Quartile 1 : 23
Median : 25
Quartile 3 : 38 <<-- change is here
Maximum : 65
IQR = 15 <<-- change is here

Answer 23

state b i got 42 not 38 ummmm.

Answer 24

i have to figure that out again hold on a sec

Answer 25

@jim_thompson5910 can you explain what i am doing wrong why im not getting 38 i took 25,26,50,65 and added them i got 166 then divided them by 4 and got 41.5 so 42

Answer 26

you aren't finding the mean, you want the median

Answer 27

sort list 2

Answer 28

ohhhhhh i had those to mixed up

Answer 29

i see now thank you
26 and 50 then divide = 38

Answer 30

yes

Answer 31

so the IQR is 15

Answer 32

correct

Answer 33

yayyy thank you and now i have to justify my answer lol

Answer 34

use the same reasoning as you did for state A

if
(distance from Q1 to median) = (distance from Q3 to median)
AND
(distance from min to median) = (distance from max to median)
then
box plot is symmetrical

Answer 35

if any of those two things are false, then the box plot is not symmetrical

Answer 36

oh thank you soooo much i understand it now

Answer 37

you're welcome