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What will be the 25th percentile of the dataset? What will be the 75th percentile of the dataset? Find IQR of the dataset 

To find the 25th percentile (Q1), 75th percentile (Q3), and the Interquartile Range (IQR) of the dataset represented by the stem and leaf diagram, we need to follow these steps:

1. List all the ages in ascending order.
2. Determine the position of the 25th and 75th percentiles.
3. Find the values at these positions.
4. Calculate the IQR by subtracting Q1 from Q3.

Let's start with listing the ages in ascending order from the stem and leaf diagram:

- Stem 1: 14, 15, 18
- Stem 2: 21, 22, 24
- Stem 3: 31, 31, 32, 33, 33, 34

So, the dataset in ascending order is:
\[ 14, 15, 18, 21, 22, 24, 31, 31, 32, 33, 33, 34 \]

There are 12 data points in total.

### Step 1: Calculate the 25th Percentile (Q1)
The formula to find the position of the 25th percentile (Q1) is:
\[ Q1 = \frac{n+1}{4} \]
where \( n \) is the number of data points.

\[ Q1 = \frac{12+1}{4} = \frac{13}{4} = 3.25 \]

Since the position is 3.25, Q1 is between the 3rd and 4th values in the dataset. To find this value, we take the 3rd value and add 0.25 of the difference between the 3rd and 4th values.

The 3rd value is 18, and the 4th value is 21:
\[ Q1 = 18 + 0.25 \times (21 - 18) = 18 + 0.75 = 18.75 \]

### Step 2: Calculate the 75th Percentile (Q3)
The formula to find the position of the 75th percentile (Q3) is:
\[ Q3 = 3 \times \frac{n+1}{4} \]

\[ Q3 = 3 \times \frac{13}{4} = \frac{39}{4} = 9.75 \]

Since the position is 9.75, Q3 is between the 9th and 10th values in the dataset. To find this value, we take the 9th value and add 0.75 of the difference between the 9th and 10th values.

The 9th value is 32, and the 10th value is 33:
\[ Q3 = 32 + 0.75 \times (33 - 32) = 32 + 0.75 = 32.75 \]

### Step 3: Calculate the Interquartile Range (IQR)
The IQR is the difference between Q3 and Q1:
\[ \text{IQR} = Q3 - Q1 = 32.75 - 18.75 = 14 \]

### Summary
- The 25th percentile (Q1) is 18.75 years.
- The 75th percentile (Q3) is 32.75 years.
- The Interquartile Range (IQR) is 14 years.

Would you like more details or have any questions?

Here are 5 related questions you might want to ask:
1. How do you interpret the interquartile range in a dataset?
2. What is the significance of the 25th and 75th percentiles?
3. How do you calculate percentiles for a larger dataset?
4. Can you explain how to create a stem and leaf diagram?
5. What are some common uses of the interquartile range in statistics?

**Tip:** Always ensure your dataset is sorted in ascending order before calculating percentiles and other statistical measures.

Learn how to calculate the 25th percentile, 75th percentile, and Interquartile Range (IQR) of a dataset with a detailed step-by-step guide. This problem involves sorting data, using percentile formulas, and interpreting statistical measures. Suitable for high school students and anyone learning data analysis.

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