URGENT
Find and interpret the range of the points earned.
Points Earned
15 12 17 8
21 20 6 9
Find and Interpret the interquartile range of the points earned.
Use the IQR to identify any outliers of the data set.
To find the range of the points earned, you need to subtract the minimum value from the maximum value in the data set.
In this case, the given data set is: 15, 12, 17, 8, 21, 20, 6, 9.
The minimum value is 6 and the maximum value is 21.
So, the range of the points earned is 21 - 6 = 15.
To find the interquartile range (IQR) of the points earned, you first need to find the first quartile (Q1) and the third quartile (Q3).
To find Q1, you need to calculate the median of the lower half of the data set. Arrange the data in ascending order: 6, 8, 9, 12. The median of this lower half is the average of the two middle values, which are 8 and 9. So, Q1 = (8 + 9) / 2 = 8.5.
To find Q3, you need to calculate the median of the upper half of the data set. Arrange the data in ascending order: 15, 17, 20, 21. The median of this upper half is the average of the two middle values, which are 17 and 20. So, Q3 = (17 + 20) / 2 = 18.5.
Now that you have Q1 and Q3, you can find the interquartile range (IQR) by subtracting Q1 from Q3. So, IQR = Q3 - Q1 = 18.5 - 8.5 = 10.
To identify any outliers using the IQR, you can consider any value that is less than Q1 - 1.5 * IQR or greater than Q3 + 1.5 * IQR as an outlier.