To find the 44th percentile (P44) from a given dataset, follow these steps:

Step 1: Arrange the data in ascending order (already given):

10.2, 10.5, 10.8, 12.3, 15.5, 17.5, 17.6, 20, 22, 23.8, 24, 24.3, 25.8, 26.7, 29.3, 30.6, 30.9, 31.9, 32.7, 33.8, 38.2, 38.6, 40.2, 40.5, 41.4, 42.2, 43.7, 45.5

Step 2: Calculate the position of P44

The formula to find the position of a percentile is: $P_k = \frac{k}{100} \times (n + 1)$ where $k$ is the percentile (44 in this case) and $n$ is the number of data points.

Here, $n = 28$ (since there are 28 data points).

Now, substitute into the formula: $P_{44} = \frac{44}{100} \times (28 + 1) = 0.44 \times 29 = 12.76$

Step 3: Locate the value at the 12.76th position

• The 12th value in the dataset is 24.3.
• The 13th value in the dataset is 25.8.

Since the position is 12.76, the 44th percentile will be closer to the 13th value but slightly below it. We can use linear interpolation to find the exact value.

$P_{44} = 24.3 + (25.8 - 24.3) \times (12.76 - 12)$ $P_{44} = 24.3 + (1.5) \times (0.76) = 24.3 + 1.14 = 25.44$

Final Answer:

$P_{44} = 25.44$

Would you like more details or have any questions?

Here are 5 related questions:

1. How do we compute other percentiles like the 75th or 90th?
2. What is the difference between percentiles and quartiles?
3. Can percentile values be used to identify outliers?
4. How does linear interpolation improve percentile calculations?
5. What role does the size of the dataset play in finding percentiles?

Tip: Always check if data is sorted before calculating percentiles; unsorted data will lead to incorrect results.