Calculating the Range and Interquartile Range
To compute the range and the interquartile range (IQR) of a data set, follow these steps:
Step 1: Organize the Data
First, arrange the data values in ascending order. For your data set:
10, 12, 16, 17, 20
Step 2: Calculate the Range
The range is the difference between the maximum and minimum values in the data set. In this case:
- Minimum Value = 10
- Maximum Value = 20
Thus, the range is calculated as follows:
Range = Maximum Value - Minimum Value = 20 - 10 = 10
Step 3: Calculate the Interquartile Range (IQR)
The IQR measures the spread of the middle 50% of the data. To find the IQR, we need to determine the first quartile (Q1) and the third quartile (Q3).
Finding Q1 and Q3:
For a data set of 5 values:
- Q1 is the median of the first half of the data (below the median)
- Q3 is the median of the second half of the data (above the median)
Given the ordered data set:
10, 12, 16, 17, 20
The median (Q2) is 16, which is the middle value. Now, identify Q1 and Q3:
- First half (Q1): 10, 12
Q1 = (10 + 12) / 2 = 11 - Second half (Q3): 17, 20
Q3 = (17 + 20) / 2 = 18.5
Now, calculate the IQR:
IQR = Q3 - Q1 = 18.5 - 11 = 7.5
Final Results
In summary, for the data values of 10, 20, 12, 17, and 16:
- Range = 10
- Interquartile Range (IQR) = 7.5