The maximum value in the student grades data set is 180. The IQR is relatively large, which means that the grades are spread out and there is a significant range of ability levels among the students.
Student Grades on a Math Assessment
| A | B | C | D | E | F | G |
|---|---|---|---|---|---|---|
| 60 | 60 | 50 | 180 | 75 | 85 | 95 | 100 | 103 |
| 84 | 86 | 88 | 89 | 84 | 70 | 89 | 99 | 104 | 99 |
Questions:
What is the minimum?
What is the maximum?
What is the range?
What is Q1?
What is the median (Q2)?
What is Q3?
What is the IQR?
Answers:
Minimum:** 50
Maximum:** 180
Range:** 180 - 50 = 130
Q1:** 75
Median (Q2):** 86
Q3:** 99
IQR:** Q3 - Q1 = 99 - 75 = 24
Minimum: The minimum value in the data set is the smallest value in the data set. In this case, the smallest value is 50.
Maximum:The maximum value in the data set is the largest value in the data set. In this case, the largest value is 180.
Range: The range is the difference between the maximum and minimum values in the data set. In this case, the range is 180 - 50 = 130.
Q1:*Q1 is the first quartile, which is the median of the lower half of the data set. In this case, the lower half of the data set is {50, 60, 60, 75, 84}. The median of this data set is 75, so Q1 is 75.
Median (Q2): The median is the middle value of the data set when the data set is sorted in ascending order. In this case, the median is 86.
Q3: Q3 is the third quartile, which is the median of the upper half of the data set. In this case, the upper half of the data set is {85, 86, 88, 89, 89, 95, 100, 103, 104, 180}. The median of this data set is 99, so Q3 is 99.
IQR:The IQR is the interquartile range, which is the difference between Q3 and Q1. In this case, the IQR is 99 - 75 = 24.
The IQR is a measure of dispersion, which means that it tells us how spread out the data is. A larger IQR means that the data is more spread out, while a smaller IQR means that the data is more clustered around the median.
In the case of the student grades, the IQR is relatively large, which means that the grades are spread out. This suggests that there is a significant range of ability levels among the students.
Box and whisker plot
A box and whisker plot is a graphical representation of the five-number summary of a data set: the minimum, Q1, median, Q3, and maximum. The box represents the middle 50% of the data, while the whiskers represent the remaining 25% of the data on each side.
Here is a box and whisker plot of the student grades data:
[Box and whisker plot of the student grades data]
The box and whisker plot shows that the median grade is 86, and the middle 50% of the grades are between 75 and 99. The whiskers show that the lowest grade is 50 and the highest grade is 180. There are a few outliers, which are points that fall outside of the whiskers.