Imagine that 11 Psych 02 students took a statistics quiz.  Using the scores given below, please calculate the following answers. 

ROUND OFF ALL DECIMALS TO 2 PLACES WHENEVER AND WHEREVER THE DECIMALS OCCUR. 

Psych 02 SCORES: 20, 7, 4, 5, 5, 8, 7, 11, 9, 10, 6Using the same data as Question 30

 

What is the Interquartile Range (IQR)

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.

Imagine that 11 Psych 02 students took a statistics quiz. Using the scores given below, please calculate the following answers. ROUND OFF ALL DECIMALS TO 2 PLACES WHENEVER AND WHEREVER THE DECIMALS OCCUR. Psych 02 SCORES: 20, 7, 4, 5, 5, 8, 7, 11, 9, 10, 6 Using the same data as Question 30. What is the Interquartile Range (IQR)?

Learn how to calculate the Interquartile Range (IQR) using the quiz scores: 20, 7, 4, 5, 5, 8, 7, 11, 9, 10, 6. This problem involves key statistical concepts such as quartiles and IQR, suitable for high school students in Grades 9-12. Step-by-step solution provided with explanation of Q1, Q3, and the IQR formula.

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