Temperature Quartiles Af4673

1. **State the problem:** We have temperature data recorded over 3 weeks (21 data points) and need to find the first quartile ($Q_1$), median ($Q_2$), and third quartile ($Q_3$). 2. **List the data:** $$\{18, 20, 23, 23, 19, 18, 15, 16, 21, 24, 28, 28, 21, 20, 22, 17, 18, 22, 26, 30, 29\}$$ 3. **Sort the data in ascending order:** $$\{15, 16, 17, 18, 18, 18, 19, 20, 20, 21, 21, 22, 22, 23, 23, 24, 26, 28, 28, 29, 30\}$$ 4. **Number of data points:** $n = 21$ 5. **Find the median ($Q_2$):** - Median position is at $\frac{n+1}{2} = \frac{21+1}{2} = 11$th data point. - The 11th data point in sorted list is $21$. 6. **Find the first quartile ($Q_1$):** - $Q_1$ is the median of the lower half (first 10 data points): $$\{15, 16, 17, 18, 18, 18, 19, 20, 20, 21\}$$ - Median position in lower half is $\frac{10+1}{2} = 5.5$th data point. - $Q_1 = \frac{18 + 18}{2} = 18$ 7. **Find the third quartile ($Q_3$):** - $Q_3$ is the median of the upper half (last 10 data points): $$\{21, 22, 22, 23, 23, 24, 26, 28, 28, 29, 30\}$$ - Actually, upper half is the 12th to 21st data points: $$\{22, 22, 23, 23, 24, 26, 28, 28, 29, 30\}$$ - Median position in upper half is $5.5$th data point. - $Q_3 = \frac{24 + 26}{2} = 25$ **Final answers:** - First quartile $Q_1 = 18$ - Median $Q_2 = 21$ - Third quartile $Q_3 = 25$