Answer:
a.
lower Quartile= 57.5
Upper Quartile=81
b.
23.5
c.
box-plot is attached in excel file
Step-by-step explanation:
The data is arranged in ascending order so, the lower quartile denoted as Q1 can be calculated as under
Q1=((n+1)/4)th score=(41/4)th score=(10.25)th score
Q1=10th score+0.25(11th-10th)score
Q1=57+0.25(59-57)=57+0.5=57.5
Q1=57.5
The data is arranged in ascending order so, the third quartile denoted as Q3 can be calculated as under
Q3=(3(n+1)/4)th score=(3*41/4)th score=(30.75)th score
Q3=30th score+0.75(31th-30th)score
Q3=81+0.75(81-81)=81+0=81
Q3=81
b)
Interquartile range=IQR=Q3-Q1=81-57.5=23.5
IQR=23.5
c)
The box-plot is made in excel and it shows no outlier. The box-plot shows the 5-number summary(minimum-Q1-median-Q3-maximum) as 25-57.5-72-81-98.
