Courtney recorded her friends' shoe sizes. 4, 8, 7, 10, 12, 9, 8, 5 What was the interquartile range of the shoe sizes? A. 3.5 B. 6.0 C. 8.0 D. 9.5

Step-by-step explanation:

Hello!

The Interquartile range (IQR) is a measurement of dispersion, it is the "distance" between the third quartile and the first quartile.

IQR = Q₃ - Q₁

Data 4, 5, 7, 8, 8, 9, 10, 12 (ordered from least to greatest)

n= 8

The first quantile separates the bottom 25% from the top 75%

First, you calculate the position of the quartile:

Position Q₁= (n+1)/4= (8+1)/4= 2.25

4, 5, 7, 8, 8, 9, 10, 12

The 1st quartile is between the 2nd and 3rd observation, so the next step is to calculate the average between the two observations to get the value of the quartile:

Q₁= (5+7)/2= 6

The third quantile separates the bottom 75% from the top 25%

First, you calculate the position of the quartile:

Position Q₃= (n+1)*(3/4)= (8+1)*(3/4)= 6.75

4, 5, 7, 8, 8, 9, 10, 12

The 3rd quartile is between the 6th and 7th observation, so the next step is to calculate the average between the two observations to get the value of the quartile:

Q₃= (9+10)/2= 9.5

IQR = Q₃ - Q₁= 9.5-6= 3.5

The correct answer is A.

I hope this helps!

arc length = 6.63311 ft.

step-by-step explanation:

the formula the arc measure is:

arc length s=2πr(c)/360

where:

c   is the central angle of the arc in degrees

r   is the radius of the arc

π   is pi, approximately 3.142

using the above formula we get

s =

thus we find that arc length of an arc for a circle of radius 20 feet and central angle 19 degrees is

6.63311 feet