Question: The percentage of points scored by Jack each year during his four year degree course is shown in the table. Which is the equivalent box-and-whisker plot for the data? Also find the average percentage of points scored by him during the course.
Year
Percentage of points
1st Year
70
2nd Year
82
3rd Year
76
4th Year
80
A ) Figure 1, 77 B ) Figure 3, 76 C ) Figure 4, 80 D ) Figure 2, 78
Steps to derive
1 The ascending order of the percentages scored by Jack is 70, 76, 80, 82.
2 In the percentages, the least value is 70 and the highest value is 82.
3 Middle quartile (Q2) = Median of all the data
[Simplify.] 4 = (76+80)2 = 1562 = 78
5 Lower quartile (Q1) = Median of lower half of the data
[Simplify.] 6 = (70+76)2 = 1462 = 73
7 Upper quartile (Q3) = Median of upper half of the data
[Simplify.] 8 = (80+82)2 = 1622 = 81
9 So, Figure 1 is the equivalent box-and-whisker plot of the data.
10 Average percentage of points = 70+76+80+824 = 77
11 Therefore, the average percentage of points scored by Jack is 77.
