Consider the following artificial data:
-10, -2, 0, 0, 0, 6, 0, 1.
Find P30.

To find the 30th percentile (\(P_{30}\)) of the given data set:

The steps are as follows:

### 1. Arrange the data in ascending order:
The given data set is:
\[
-10, -2, 0, 0, 0, 6, 0, 1
\]

When arranged in ascending order:
\[
-10, -2, 0, 0, 0, 0, 1, 6
\]

### 2. Use the percentile formula:
For any percentile \(P_k\), the position \(n_k\) is determined by the formula:
\[
n_k = \frac{k}{100} \times (N+1)
\]
where:
- \(k\) is the percentile (here, \(k = 30\)),
- \(N\) is the total number of data points (here, \(N = 8\)).

Substitute into the formula:
\[
n_{30} = \frac{30}{100} \times (8 + 1) = 0.30 \times 9 = 2.7
\]

### 3. Interpretation of the position:
The result \(n_{30} = 2.7\) indicates that the 30th percentile lies between the 2nd and 3rd values in the sorted data. To calculate \(P_{30}\), we interpolate between these two values.

- The 2nd value is \(-2\).
- The 3rd value is \(0\).

### 4. Interpolation:
To interpolate between the 2nd and 3rd values:
\[
P_{30} = \text{2nd value} + (\text{fractional part of } n_{30}) \times (\text{3rd value} - \text{2nd value})
\]
\[
P_{30} = -2 + (0.7) \times (0 - (-2)) = -2 + 0.7 \times 2 = -2 + 1.4 = -0.6
\]

Thus, the 30th percentile (\(P_{30}\)) is \(-0.6\).

Would you like more details on any step?

### 5 Related Questions:
1. What is the interpretation of the 30th percentile in this context?
2. How do you calculate other percentiles (e.g., \(P_{50}\)) using similar steps?
3. What does it mean if multiple values are the same in the data set when calculating percentiles?
4. How would the result change if the data set were larger?
5. Can percentiles be calculated for non-numeric data?

**Tip:** Always ensure the data is sorted before calculating percentiles to avoid mistakes.

Consider the following artificial data -10, -2, 0, 0, 0, 6, 0, 1. Find P30.

Learn how to find the 30th percentile (P30) of the data set [-10, -2, 0, 0, 0, 6, 0, 1] using percentile and interpolation formulas. Understand the detailed steps of arranging the data and applying statistical methods to solve the problem. Ideal for students in Grades 10-12.

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