Question

The table below shows the number of hours some college athletes in two states spend on indoor sports each week:

State A 7 9 5 4 25 21 6 6 8
State B 14 12 10 13 15 14 11 15 16

Part A: Create a five-number summary and calculate the interquartile range for the two sets of data. (6 points)

Part B: Are the box plots symmetric? Justify your answer. (4 points)

Answer 1

@Vocaloid

Answer 2

five number summary = min, Q1, median, Q3, max

start with state A, find the min, max, and median.

Answer 3

start by arranging the data values from least to greatest

Answer 4

so for state a
4-min
4-Q1
7-median
21-Q3
25-max

Answer 5

check your Q1 again

Answer 6

actually check both your Q1 and Q3 again

Answer 7

sorry i meant 5

Answer 8

putting the #'s in order we get

4 5 6 6 7 8 9 21 25

the median is 7, now we take the data points above 7 and below 7 and separate them

4 5 6 6

and

8 9 21 25

calculate the median of these two sets

Answer 9

*medians*

Answer 10

for the first set the median is 5.5 for the second its 15

Answer 11

good so

4-min
5.5 - Q1
7-median
15-Q3
25-max

Answer 12

now repeat with state (b), remember that the median is excluded when separating the data for Q1 and Q3 calculations

Answer 13

so for state b
10-min
11.5-Q1
14-median
15-Q3
16-max

Answer 14

good

now for the second part of part A, to calculate the interquartile range for each state you just need to subtract Q3 - Q1

Answer 15

for each state?

Answer 16

yes

Answer 17

so state a- 9.5-IQR
state b-3.5-IQR

Answer 18

good so that's part A done

for part B you can try sketching out the box plot to see if both sides are roughly symmetric or not

http://www.alcula.com/calculators/statistics/box-plot/

Answer 19

hm

Answer 20

state b is more then state a

Answer 21

is more symmetric

Answer 22

good, neither of them are really super symmetric but b is more symmetric than a

for the justification, you could note that for state a) (Q1 - max) is bigger than (max - Q3) making the lower whisker much larger than the upper whisker

for state b) the whiskers are closer together in length, but the right side of the box (Q3-median) is much larger than the left side of the box (median - Q1)

Answer 23

okay thank you so much