To compute the range and interquartile range (IQR) for the given data values of 10, 20, 12, 17, and 16, we will follow these steps:
Step 1: Compute the Range
The range is calculated by subtracting the smallest value in the data set from the largest value.
- Largest value: 20
- Smallest value: 10
So, the range is:
Range = Largest value – Smallest value = 20 – 10 = 10
Step 2: Compute the Interquartile Range (IQR)
The IQR is the difference between the first (Q1) and third quartiles (Q3) of the data set. First, we need to arrange the data in ascending order:
- Arranged data: 10, 12, 16, 17, 20
Next, we find Q1 and Q3:
- Q1 (the first quartile) is the median of the first half of the data:
- For the values 10, 12 (the first half), Q1 is 11.
- Q3 (the third quartile) is the median of the second half of the data:
- For the values 16, 17, 20 (the second half), Q3 is 17.
Finally, we can calculate the IQR:
IQR = Q3 – Q1 = 17 – 11 = 6
Conclusion
So, for the given data values, the Range is 10 and the Interquartile Range is 6.