Use the following data to answer questions 11 - 26

Score z-score Percentile
52
50
43
38
38
37
35
35
35
28
27
27
25
23

The interquartile range for the Score column is _______________.

Group of answer choices

13

14

11

12

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.

The interquartile range for the Score column is _______________.

Learn how to calculate the interquartile range (IQR) for a given dataset. This example uses scores ranging from 23 to 52 and walks through the steps of finding Q1 and Q3 to compute the IQR. Suitable for high school students in Grades 10-12.

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