Let's analyze the data given and find the measures of dispersion.

Data Given:

The data is: $12.2, 11.5, 12.1, 12.2, 12.2, 12.1, 12.5, 12.1, 11.7$

Step 1: Sort the Data

Sorted dataLet's analyze the data given and find the measures of dispersion.

Data Given:

The data is: $12.2, 11.5, 12.1, 12.2, 12.2, 12.1, 12.5, 12.1, 11.7$

Step 1: Sort the Data

Sorted $11.5, 11.7, 12.1, 12.1, 12.1, 12.2, 12.2, 12.2, 12.5$

Step 2: Calculate the Measures

1. Minimum: The smallest value in the data is $11.5$.
2. Quartile 1 (Q1): This is the median of the lower half of the data (first 4 values in sorted data).
   • Lower half: $11.5, 11.7, 12.1, 12.1$
   • Q1 = median of lower half = $11.9$.
3. Median: The median of the entire dataset.
   • Since there are 9 values, the median is the 5th value in sorted data, which is $12.1$.
4. Quartile 3 (Q3): This is the median of the upper half of the data (last 4 values in sorted data).
   • Upper half: $12.2, 12.2, 12.2, 12.5$
   • Q3 = median of upper half = $12.2$.
5. Maximum: The largest value in the data is $12.5$.
6. Range: The difference between the maximum and minimum values.
   • Range = $12.5 - 11.5 = 1.0$.
7. Interquartile Range (IQR): The difference between Q3 and Q1.
   • IQR = $12.2 - 11.9 = 0.3$.

Summary

• Minimum: $11.5$
• Quartile 1 (Q1): $11.9$
• Median: $12.1$
• Quartile 3 (Q3): $12.2$
• Maximum: $12.5$
• Range: $1.0$
• Interquartile Range (IQR): $0.3$

Would you like more details on any of these calculations?

Further Questions

1. How are quartiles calculated for different sample sizes?
2. What is the importance of interquartile range in data analysis?
3. How can outliers affect the range and interquartile range?
4. What is the difference between range and interquartile range?
5. Why is the median often preferred over the mean in data analysis?

Tip

The interquartile range is useful for identifying the spread of the middle 50% of your data, minimizing the impact of outliers.