Question

Below are the ratings for a sample of 12 hotels in small Ontario towns:

Answer 1

Answer:

a)

i) Interquartile range is   2.4  

ii) Upper boundary is 10.8  

The Lower boundary is 1.2  

iii) Outliers are points above the upper boundary or below the lower boundary  

There is one outlier: 1.1

b) The modified boxplot with one outlier is given in the diagram.                                                          

c) The 80th percentile is    

The minimum rating the hotel can get is 7.3

Step-by-step explanation:

a)

i) Interquartile range is  

IQR = Q3-Q1 = 7.2-4.8 = 2.4  

ii) Upper boundary = Q3+ 1.5 *IQR = 7.2+1.5*2.4 = 10.8  

Lower boundary = Q1 - 1.5*IQR = 4.8- 1.5*2.4 = 1.2  

iii) Outliers are points above the upper boundary or below the lower boundary  

There is one outlier: 1.1  

c) The 80th percentile is given by  

n= 12  

k = 0.80  

Index is given by k*n =0.80*12 = 9.6  

Round to nearest whole number, that is 10th  

80th percentile is the 10th number (arranged in ascending order)  

80th percentile = 7.3  

The minimum rating the hotel can get is 7.3.

b) The modified boxplot with one outlier is given as follows,