Quartile Deviation Ab5194

1. **State the problem:** Find the quartile deviation for the data set $16, 42, 6, 20, 28, 23, 15$. 2. **Arrange the data in ascending order:** $$6, 15, 16, 20, 23, 28, 42$$ 3. **Find the median (Q2):** Since there are 7 data points (odd number), the median is the middle value, which is the 4th value: $$Q2 = 20$$ 4. **Find the lower quartile (Q1):** Q1 is the median of the lower half (values before the median): Lower half: $6, 15, 16$ Median of lower half is the 2nd value: $$Q1 = 15$$ 5. **Find the upper quartile (Q3):** Q3 is the median of the upper half (values after the median): Upper half: $23, 28, 42$ Median of upper half is the 2nd value: $$Q3 = 28$$ 6. **Calculate the quartile deviation (QD):** Formula: $$QD = \frac{Q3 - Q1}{2}$$ Substitute values: $$QD = \frac{28 - 15}{2} = \frac{13}{2} = 6.5$$ 7. **Final answer:** The quartile deviation for the data set is **6.5**.