21, 31, 33, 41, 18, 27, 52, 62, 72, 73, 69, 55, 37, 31, 18, 22,

25, 26, 29, 30, 36, 37, 42, 47, 58, 64, 57, 77, 76, 74, 71, 67 find third decile

To find the third decile (D₃), we follow these steps:

### Step 1: Arrange the data in ascending order.

The data in ascending order is:
\[ 18, 18, 21, 22, 25, 26, 27, 29, 30, 31, 31, 33, 36, 37, 37, 41, 42, 47, 52, 55, 57, 58, 62, 64, 67, 69, 71, 72, 73, 74, 76, 77 \]

### Step 2: Determine the position of the third decile.

The formula to find the position of the third decile is:
\[
D_3 = \left( \frac{3}{10} \times N \right)
\]
Where \(N\) is the total number of observations.

Here, \(N = 32\). So,
\[
D_3 = \frac{3}{10} \times 32 = 9.6
\]

### Step 3: Find the value of the third decile.

The position \(9.6\) means the third decile is between the 9th and 10th values in the ordered data.

From the ordered list:
- The 9th value is **30**
- The 10th value is **31**

Thus, the third decile (D₃) is between 30 and 31. To find the exact value, we can interpolate:
\[
D_3 = 30 + 0.6 \times (31 - 30) = 30.6
\]

### Conclusion:
The third decile (D₃) is **30.6**.

Would you like further details or clarifications?

### Related Questions:
1. How do you calculate the first and second deciles for the same data?
2. What is the median (5th decile) of the dataset?
3. How would you calculate the quartiles for this dataset?
4. Can we use another method to calculate deciles?
5. How do we apply this process to continuous data?

**Tip:** Deciles divide data into 10 equal parts, just like quartiles divide into 4 parts, and percentiles divide into 100 parts.

21, 31, 33, 41, 18, 27, 52, 62, 72, 73, 69, 55, 37, 31, 18, 22, 25, 26, 29, 30, 36, 37, 42, 47, 58, 64, 57, 77, 76, 74, 71, 67 find third decile

This guide explains how to find the third decile (D₃) of a dataset. We use the formula D₃ = (3/10) × N and apply linear interpolation for accuracy. Learn step-by-step how to organize data and perform decile calculations. Suitable for Grades 9-12 students.

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