what is the iqr of this data? 10,	13,	15,	12,	12,	4, 	12,	17,   12	13	15	18	10	11	20	19

To find the Interquartile Range (IQR) of the data, follow these steps:

### Step 1: Organize the data in ascending order.
The given dataTo find the Interquartile Range (IQR) of the data, follow these steps:

### Step 1: Organize the data in ascending order.
The given  
\[ 10, 13, 15, 12, 12, 4, 12, 17, 12, 13, 15, 18, 10, 11, 20, 19 \]

Sorted dataTo find the Interquartile Range (IQR) of the data, follow these steps:

### Step 1: Organize the data in ascending order.
The given  
\[ 10, 13, 15, 12, 12, 4, 12, 17, 12, 13, 15, 18, 10, 11, 20, 19 \]

Sorted 
\[ 4, 10, 10, 11, 12, 12, 12, 12, 13, 13, 15, 15, 17, 18, 19, 20 \]

### Step 2: Find the quartiles.

- **Q1** (1st quartile) is the median of the lower half (excluding the overall median if the data size is odd).
  The lower half of the dataTo find the Interquartile Range (IQR) of the data, follow these steps:

### Step 1: Organize the data in ascending order.
The given  
\[ 10, 13, 15, 12, 12, 4, 12, 17, 12, 13, 15, 18, 10, 11, 20, 19 \]

Sorted 
\[ 4, 10, 10, 11, 12, 12, 12, 12, 13, 13, 15, 15, 17, 18, 19, 20 \]

### Step 2: Find the quartiles.

- **Q1** (1st quartile) is the median of the lower half (excluding the overall median if the data size is odd).
  The lower half of the 
  \[ 4, 10, 10, 11, 12, 12, 12, 12 \]
  Median of this lower half (Q1) is:
  \[ Q1 = \frac{11 + 12}{2} = 11.5 \]

- **Q3** (3rd quartile) is the median of the upper half.
  The upper half of the dataTo find the Interquartile Range (IQR) of the data, follow these steps:

### Step 1: Organize the data in ascending order.
The given  
\[ 10, 13, 15, 12, 12, 4, 12, 17, 12, 13, 15, 18, 10, 11, 20, 19 \]

Sorted 
\[ 4, 10, 10, 11, 12, 12, 12, 12, 13, 13, 15, 15, 17, 18, 19, 20 \]

### Step 2: Find the quartiles.

- **Q1** (1st quartile) is the median of the lower half (excluding the overall median if the data size is odd).
  The lower half of the 
  \[ 4, 10, 10, 11, 12, 12, 12, 12 \]
  Median of this lower half (Q1) is:
  \[ Q1 = \frac{11 + 12}{2} = 11.5 \]

- **Q3** (3rd quartile) is the median of the upper half.
  The upper half of the 
  \[ 13, 13, 15, 15, 17, 18, 19, 20 \]
  Median of this upper half (Q3) is:
  \[ Q3 = \frac{15 + 15}{2} = 15 \]

### Step 3: Calculate the IQR.

\[
\text{IQR} = Q3 - Q1 = 15 - 11.5 = 3.5
\]

Thus, the **Interquartile Range (IQR)** is **3.5**.

Would you like more details on the steps?

### Relative Questions:
1. How is the interquartile range used to detect outliers?
2. Can the IQR be used for non-numeric data?
3. What is the difference between the IQR and the standard deviation?
4. How does IQR change if there are repeated values in the dataset?
5. How would the IQR differ if we changed one value in the dataset?

### Tip:
The IQR is resistant to outliers, making it a great tool for understanding the spread of the middle 50% of your data.

what is the iqr of this data? 10, 13, 15, 12, 12, 4, 12, 17, 12, 13, 15, 18, 10, 11, 20, 19

Learn how to calculate the Interquartile Range (IQR) for the dataset: 10, 13, 15, 12, 12, 4, 12, 17, 12, 13, 15, 18, 10, 11, 20, 19. This detailed solution covers how to find Q1 and Q3, providing a step-by-step explanation suitable for students in Grades 9-12.

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