To calculate the Interquartile Range (IQR), follow these steps:

Step 1: Organize the scores in ascending order.

Scores: $4, 5, 5, 6, 7, 7, 8, 9, 10, 11, 20$

Step 2: Find the quartiles (Q1 and Q3).

• Q1 (first quartile): This is the median of the lower half of the data (excluding the median if the data set size is odd).
  • Lower half of the dataTo calculate the Interquartile Range (IQR), follow these steps:

Step 1: Organize the scores in ascending order.

Scores: $4, 5, 5, 6, 7, 7, 8, 9, 10, 11, 20$

Step 2: Find the quartiles (Q1 and Q3).

• Q1 (first quartile): This is the median of the lower half of the data (excluding the median if the data set size is odd).

  • Lower half of the
    $4, 5, 5, 6, 7$
  • The middle value (median of the lower half) is 5, so: $Q1 = 5$

• Q3 (third quartile): This is the median of the upper half of the data (excluding the median if the data set size is odd).

  • Upper half of the dataTo calculate the Interquartile Range (IQR), follow these steps:

Step 1: Organize the scores in ascending order.

Scores: $4, 5, 5, 6, 7, 7, 8, 9, 10, 11, 20$

Step 2: Find the quartiles (Q1 and Q3).

• Q1 (first quartile): This is the median of the lower half of the data (excluding the median if the data set size is odd).

  • Lower half of the
    $4, 5, 5, 6, 7$
  • The middle value (median of the lower half) is 5, so: $Q1 = 5$

• Q3 (third quartile): This is the median of the upper half of the data (excluding the median if the data set size is odd).

  • Upper half of the
    $8, 9, 10, 11, 20$
  • The middle value (median of the upper half) is 10, so: $Q3 = 10$

Step 3: Calculate the Interquartile Range (IQR).

$\text{IQR} = Q3 - Q1 = 10 - 5 = 5$

Conclusion:

The Interquartile Range (IQR) is 5.

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Would you like more details on quartiles or any further explanation?

Here are 5 related questions you might find useful:

1. How do you calculate the median for an odd number of data points?
2. What is the significance of the IQR in statistics?
3. How do you handle outliers when calculating quartiles?
4. Can you compare IQR with the standard deviation as a measure of variability?
5. How can skewness affect the interquartile range?

Tip: The IQR is resistant to outliers, making it a robust measure of spread in skewed distributions.