Amanda, Derrick, and Todd attend the same high school. Each student works as the cashier one night a week at the school's concession stand.
The number of items sold at the concession stand to the first 20 customers on three different nights is represented on the dot plots below.
Dot plot graph on items sold at the concession stands for Amanda, Derrick, and Todd. The number line represents No of items sold ranging from 0 to 8. Circles on numbers represent first 20 customers.
Find the interquartile range, IQR, for each dot plot. Then, place the students in order from greatest to least IQR.
Amanda
Derrick
Todd
> >
First, we need to find the quartiles for each dot plot. Quartiles separate the data set into four equal parts.
For Amanda:
Q1 = 3
Q2 (median) = 5
Q3 = 7
For Derrick:
Q1 = 4
Q2 (median) = 6
Q3 = 7
For Todd:
Q1 = 2
Q2 (median) = 4
Q3 = 6
Next, we calculate the IQR for each student by finding the difference between Q3 and Q1:
For Amanda: IQR = Q3 - Q1 = 7 - 3 = 4
For Derrick: IQR = Q3 - Q1 = 7 - 4 = 3
For Todd: IQR = Q3 - Q1 = 6 - 2 = 4
Finally, we arrange the students in order from greatest to least IQR:
1. Amanda - IQR = 4
2. Todd - IQR = 4
3. Derrick - IQR = 3
Therefore, the order from greatest to least IQR is:
Amanda > Todd > Derrick