QUARTILES—HAND CALCULATIONS AND THE SOFTWARE OUTPUT
Range, Quartiles, Interquartile range, and the Software Output (SPSS, Excel, and Python)
September 25, 2025
The Range and the Inter-Quartile Range (IQR) are the measures that describe the spread of data.
A tracking sheet includes the years of relevant job experience for various posts.
5, 7, 4, 6, 8, 9, 4
Let’s arrange the data in ascending order.
RANGE
The range of a data set is the difference between the highest (maximum) and lowest (minimum) values.
Range = Maximum value - Minimum value
Range = 9 - 4 = 5 years
QUARTILES
The 2nd Quartile (Q2) or the middle quartile is the median. It is the middle value that divides the data into two equal parts.
The 1st Quartile (Q1) or the lower quartile (QL) separates the lower quarter of values from the rest of the values. This is the value at the middle point of the first half of the data.
The 3rd Quartile (Q3) or the upper quartile (QU) separates the upper quarter of values from the rest of the values. This is the value at the middle point of the second half of the data.
INTER QUARTILE RANGE (IQR)
It is the difference between the upper quartile (Q3 or QU) and the lower quartile (Q1 or QL)
IQR = QU - QL
IQR = 7.5 - 4.5 = 3 years
QUARTILES IN SOFTWARE OUTPUT
The table summarizes the quartile values calculated by the pre-defined functions of computer software.
| Computer Software | Q1 | Q2 | Q3 |
|---|---|---|---|
| SPSS (Tukey's Hinges) | 4.5 | 6 | 7.5 |
| Excel (Quartile) | 4.5 | 6 | 7.5 |
| Python (Quantile) | 4.5 | 6 | 7.5 |
Values of the open positions variable on a Job recruitment sheet are:
6, 7, 5, 12, 9, 10
Let’s arrange the data in ascending order.
RANGE
Range = Maximum value - Minimum value
Range = 12 - 5 = 7
QUARTILES
The 2nd Quartile (Q2) or the middle quartile is the median
The 1st Quartile (Q1) or the lower quartile (QL)
The 3rd Quartile (Q3) or the upper quartile (QU)
INTER QUARTILE RANGE (IQR)
It is the difference between the upper quartile (Q3 or QU) and the lower quartile (Q1 or QL)
IQR = QU - QL
IQR = 10 - 6 = 4
QUARTILES IN SOFTWARE OUTPUT
The table summarizes the quartile values calculated by the pre-defined functions of computer software.
| Computer Software | Q1 | Q2 | Q3 |
|---|---|---|---|
| SPSS (Tukey's Hinges) | 6 | 8 | 10 |
| Excel (Quartile) | 6.25 | 8 | 9.75 |
| Python (Quantile) | 6.25 | 8 | 9.75 |
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