Question

Help please?
The five-number summary of scores on a test is

35 60 65 70 90

Based on this information,
A. there are no outliers.
B. there are low outliers.
C. there are both high and low outliers.

Answer 1

It seems like both 35 and 90 are, but it could just be 35 since it's 5 more than the difference between 70 and 90

Answer 2

the interquartile range (IQR) is

IQR = Q3 - Q1

IQR = 70 - 60

IQR = 10

Answer 3

anything greater than

m + 1.5*IQR

(where m is the median)

is considered an outlier

Answer 4

in this case

m = 65
IQR = 10

so,

m + 1.5*IQR = 65 + 1.5*10 = 80

because 90 is larger than 80, we know that 90 is an outlier

Answer 5

it works the same in the other direction as well

anything smaller than m - 1.5*IQR is considered an outlier

Answer 6

wait wouldn't Q1 equal the average of the left side of the median which is (60+35)/2 ?

Answer 7

no, the five number summary is

min, Q1, median, Q3, max

so the second value is Q1

Answer 8

so it'd be both 90 and 35 right?

Answer 9

and thanks for explaining the 5 number summary :)

Answer 10

correct, you have 2 outliers (one too low, the other too high)

Answer 11

and yw