Answer
Check Explanation
Step-by-step explanation
A) We are asked to describe the shape of the distribution of Plot A.
From the dotplot, we can see that the variables of the dataset are more concentrated on the right hand side. Indicating that the mean of this almost normal distribution is greater than its median. So, the shape of the distribution is a positively skewed normal distribution.
B) We are asked to determine which distribution has the larger median.
Plot A has the distribution
10, 15, 16, 18, 18, 18, 19, 19, 20, 20
The median is the variable at the middle of the distribution when they are arranged in ascending or descending order.
Median = [(N + 1)/2] th variable
= [(10 + 1)/2] = (11/2) = 5.5th variable
Median = [(5th variable) + (6th variable)]/2
= (18 + 18)/2
= 18
Plot B has the distribution
10, 13, 15, 15, 15, 16, 17, 18, 19, 20
Median = [(N + 1)/2] th variable
= [(10 + 1)/2] = (11/2) = 5.5th variable
Median = [(5th variable) + (6th variable)]/2
= (15 + 16)/2
= 15.5
We can see that the Restaurant A has the larger median.
C) We are asked to calculate the Inner Quartile Range for Restaurant B
IQR = (Upper Quartile) - (Lower Quartile)
Lower Quartile = [(N + 1)/4] th variable
= [(10 + 1)/4] = (11/4) = 2.75 th variable
Lower Quartile = [(2nd variable) + (3rd variable)]/2
= (13 + 15)/2
= 14
Upper Quartile = [3(N + 1)/4] th variable
= [3(10 + 1)/4] = (33/4) = 8.25 th variable
Upper Quartile = [(8th variable) + (9th variable)]/2
= (18 + 19)/2
= 18.5
IQR = (Upper Quartile) - (Lower Quartile)
= 18.5 - 14
= 4.5
Hope this Helps!!!