Answer:
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!