Interquartile Range 88Ba99

1. **State the problem:** We are given a list of 23 data points representing the time spent by pupils practising times tables. We need to find the interquartile range (IQR), which is the difference between the third quartile ($Q_3$) and the first quartile ($Q_1$). 2. **List the data in order:** The data is already ordered: $$3,4,4,4,5,5,8,8,9,9,10,12,14,14,15,15,16,16,17,19,20,20,20$$ 3. **Find the position of $Q_1$ and $Q_3$:** - Number of data points, $n = 23$ - The median position is at $\frac{n+1}{2} = \frac{23+1}{2} = 12$th value. - $Q_1$ is the median of the lower half (first 11 values). - $Q_3$ is the median of the upper half (last 11 values). 4. **Find $Q_1$:** Lower half data (first 11 values): $$3,4,4,4,5,5,8,8,9,9,10$$ Median position in lower half: $\frac{11+1}{2} = 6$th value. So, $Q_1 = 5$ 5. **Find $Q_3$:** Upper half data (last 11 values): $$12,14,14,15,15,16,16,17,19,20,20,20$$ Note: Actually, since $n=23$, the median is the 12th value (which is 12), so the upper half starts from the 13th value. Upper half data (values 13 to 23): $$14,14,15,15,16,16,17,19,20,20,20$$ Median position in upper half: $\frac{11+1}{2} = 6$th value. So, $Q_3$ is the 6th value in this list: $16$ 6. **Calculate the interquartile range:** $$IQR = Q_3 - Q_1 = 16 - 5 = 11$$ **Final answer:** $$\boxed{11}$$ minutes