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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 and interpret the range of the points earned, you simply need to subtract the minimum value from the maximum value in the dataset.
Given the data:
Points Earned: 15, 12, 17, 8, 21, 20, 6, 9
Step 1: Find the minimum value
The minimum value in the dataset is 6.
Step 2: Find the maximum value
The maximum value in the dataset is 21.
Step 3: Calculate the range
To calculate the range, subtract the minimum value from the maximum value:
Range = maximum value - minimum value
Range = 21 - 6
Range = 15
Therefore, the range of the points earned is 15.
To find and interpret the interquartile range (IQR) of the points earned, follow these steps:
Step 1: Order the data
Order the data points in ascending order:
6, 8, 9, 12, 15, 17, 20, 21
Step 2: Find the median
Calculate the median of the ordered data. Since there are 8 data points, the median will be the average of the 4th and 5th values.
Median = (12 + 15) / 2
Median = 13.5
Step 3: Find the lower quartile (Q1)
Find the median of the lower half of the data. In this case, the lower half consists of the values 6, 8, 9, and 12.
Q1 = (8 + 9) / 2
Q1 = 8.5
Step 4: Find the upper quartile (Q3)
Find the median of the upper half of the data. In this case, the upper half consists of the values 15, 17, 20, and 21.
Q3 = (17 + 20) / 2
Q3 = 18.5
Step 5: Calculate the IQR
To calculate the IQR, subtract Q1 from Q3:
IQR = Q3 - Q1
IQR = 18.5 - 8.5
IQR = 10
Therefore, the interquartile range (IQR) of the points earned is 10.
To identify any outliers using the IQR, any data point that falls below Q1 - 1.5 * IQR or above Q3 + 1.5 * IQR can be considered an outlier. In this case, any data point below 8.5 - 1.5 * 10 or above 18.5 + 1.5 * 10 would be considered an outlier.