To calculate the interquartile range (IQR) for the Score column, we first need to find the first quartile (Q1) and the third quartile (Q3) and then compute the difference between them:

$\text{IQR} = Q3 - Q1$

Step 1: Organize the data in ascending order.

Scores (sorted): 23, 25, 27, 27, 28, 35, 35, 35, 37, 38, 38, 43, 50, 52

There are 14 data points in total.

Step 2: Find Q1 and Q3.

• Q1 (25th percentile) is the value that marks the first quartile, which is the median of the lower half of the data (excluding the overall median).
• Q3 (75th percentile) is the value that marks the third quartile, which is the median of the upper half of the data.

Lower half (first 7 scores):

23, 25, 27, 27, 28, 35, 35

• The median of this lower half (Q1) is 27.

Upper half (last 7 scores):

35, 37, 38, 38, 43, 50, 52

• The median of this upper half (Q3) is 38.

Step 3: Calculate the IQR.

$\text{IQR} = Q3 - Q1 = 38 - 27 = 11$

The interquartile range is 11.

So, the correct answer is:

• 11

Would you like more details or have any further questions?

5 Related Questions:

1. How is the interquartile range different from the standard deviation?
2. What is the median score of the data provided?
3. How do quartiles divide a dataset, and what is their significance?
4. What happens to the IQR if outliers are present in the data?
5. How can the IQR be used to detect outliers in a dataset?

Tip:

The interquartile range (IQR) is a robust measure of variability and is less sensitive to outliers than standard deviation.