Question: find the interquartile range of $21$ $24$ $25$ $28$ $31$ $33$ $34$ $36$ $38$ $39$ $41$ $42$ $44$ $45$ $47$ $49$ $52$ $53$ $55$ $58$ $60$ $62$ $64$

1. **State the problem:** Find the interquartile range (IQR) of the data set: $21, 24, 25, 28, 31, 33, 34, 36, 38, 39, 41, 42, 44, 45, 47, 49, 52, 53, 55, 58, 60, 62, 64$. 2. **Sort the data:** The data is already sorted in ascending order. 3. **Count the number of data points:** There are $n = 23$ data points. 4. **Find the median (Q2):** Since $n$ is odd, median is the middle value at position $\frac{n+1}{2} = \frac{23+1}{2} = 12$. Median $Q2 = 42$ (the 12th value). 5. **Find the lower quartile (Q1):** This is the median of the lower half (first 11 values): $21, 24, 25, 28, 31, 33, 34, 36, 38, 39, 41$. Median position for lower half: $\frac{11+1}{2} = 6$. So, $Q1 = 33$ (6th value in lower half). 6. **Find the upper quartile (Q3):** This is the median of the upper half (last 11 values): $42, 44, 45, 47, 49, 52, 53, 55, 58, 60, 62, 64$. Actually, since median is 42 at position 12, upper half is from position 13 to 23: $44, 45, 47, 49, 52, 53, 55, 58, 60, 62, 64$. Median position for upper half: $\frac{11+1}{2} = 6$. So, $Q3 = 53$ (6th value in upper half). 7. **Calculate the interquartile range (IQR):** $$\text{IQR} = Q3 - Q1 = 53 - 33 = 20$$ **Final answer:** The interquartile range of the data set is $20$.