Calculating Quartiles from Sorted Data
To solve for the lower quartile, median, and upper quartile, we first need to arrange the data in ascending order, which is already done for us: 2, 6, 6, 7, 9.
The median is the middle number when the data is ordered from least to greatest. In this case, since there are five numbers, the median will be the third number:
Median = 6
The lower quartile (Q1) is the median of the lower half of the data. Since there are 5 data points, we will consider the lower half to be the first two numbers (2 and 6). The median of these two numbers is:
Lower quartile = (2 + 6) / 2 = 8 / 2 = 4
The upper quartile (Q3) is the median of the upper half of the data. For the upper half, we take the last two numbers (7 and 9). The median of these is:
Upper quartile = (7 + 9) / 2 = 16 / 2 = 8
Now we have our three values:
- Lower quartile = 4
- Median = 6
- Upper quartile = 8
