Let's break down the data analysis step by step, starting with arranging the data in ascending order, then calculating the required statistics.

Given dataLet's break down the data analysis step by step, starting with arranging the data in ascending order, then calculating the required statistics.

Given 4.9, 2.9, 3.4, 9.6, 5.7, 11.8, 9.3, 17.5, 10.9, 1.6, 8.6

Step 1: Sort the Data

The data in ascending order is: 1.6, 2.9, 3.4, 4.9, 5.7, 8.6, 9.3, 9.6, 10.9, 11.8, 17.5

Step 2: Calculate the Required Values

• Low (minimum value):
  The lowest value in the dataset is 1.6.

• Q1 (First Quartile):
  Q1 is the median of the first half of the data. Since we have 11 data points, the lower half is:
  1.6, 2.9, 3.4, 4.9, 5.7
  The median of this set (Q1) is 3.4.

• MD (Median):
  The median (MD) is the middle value of the full dataset. The 6th value is 8.6.

• Q3 (Third Quartile):
  Q3 is the median of the upper half of the data. The upper half is:
  9.3, 9.6, 10.9, 11.8, 17.5
  The median of this set (Q3) is 10.9.

• High (maximum value):
  The highest value in the dataset is 17.5.

• IQR (Interquartile Range):
  IQR = Q3 - Q1 = 10.9 - 3.4 = 7.5.

Summary of Results:

• Low = 1.6
• Q1 = 3.4
• MD = 8.6
• Q3 = 10.9
• High = 17.5
• IQR = 7.5

Would you like more details or have any other questions?
Here are 5 related questions to explore:

1. How is the interquartile range useful in data analysis?
2. What is the significance of the quartiles in a data set?
3. How would the inclusion of an outlier affect the median?
4. How can the IQR be used to identify potential outliers in the data?
5. How does the IQR compare to the standard deviation as a measure of spread?

Tip: The IQR is a robust measure of spread, particularly effective when dealing with skewed data or outliers.