To compute the interquartile range (IQR) and the coefficient of quartile deviation (QD), we first need to follow these steps:

1. Arrange the data in ascending order.
2. Find the quartiles (Q1 and Q3):
   • $Q1$ is the median of the lower half of the data.
   • $Q3$ is the median of the upper half of the data.
3. Calculate the interquartile range (IQR): $IQR = Q3 - Q1$.
4. Calculate the quartile deviation (QD): $QD = \frac{IQR}{2}$.
5. Calculate the coefficient of quartile deviation: $\text{Coefficient of QD} = \frac{Q3 - Q1}{Q3 + Q1}$.

Let's calculate these step by step.

Step 1: Arrange the data in ascending order

The given data is: $23, 25, 8, 10, 9, 29, 45, 85, 10, 16$

Arranging it in ascending order: $8, 9, 10, 10, 16, 23, 25, 29, 45, 85$

Step 2: Find Quartiles

• Q1 (First Quartile): Median of the lower half $8, 9, 10, 10, 16$
• Q3 (Third Quartile): Median of the upper half $23, 25, 29, 45, 85$

Now, I'll calculate the quartiles, interquartile range, quartile deviation, and the coefficient of QD.Here are the results:

1. First Quartile (Q1): 10.0
2. Third Quartile (Q3): 28.0
3. Interquartile Range (IQR): 18.0
4. Quartile Deviation (QD): 9.0
5. Coefficient of Quartile Deviation: 0.474 (approximately)

Would you like more details on any of these calculations or how they relate to data dispersion?

Related Questions:

1. How is the quartile deviation useful in understanding data spread?
2. What is the significance of the coefficient of quartile deviation in statistics?
3. How does the interquartile range compare with other measures of dispersion, like standard deviation?
4. Can you apply this method to a different set of data?
5. How do outliers affect the calculation of quartiles and the interquartile range?

Tip:

The interquartile range is less sensitive to outliers compared to the range because it focuses on the middle 50% of the data, making it a robust measure of spread.