The image contains a dataset, and the task is to find the data value that represents the 74th percentile (P74) from the following data:

1200, 1300, 1900, 3200, 4000,
4600, 4700, 4800, 4900, 5200,
5300, 5400, 6200, 6400, 6500,
6800, 7000, 7300, 7900, 8300,
8600.

To calculate the 74th percentile, we need to first sort the data in ascending order and use the following formula:

$P_k = \frac{k}{100} \times (n + 1)$

Where:

• $k$ is the desired percentile (74 in this case).
• $n$ is the number of data points (there are 20 data points).

The position of the 74th percentile is:

$P_{74} = \frac{74}{100} \times (20 + 1)$

This will give us the position in the sorted data, and we can find the corresponding value.

Let me calculate this for you. numpy as np

Given data

data = [1200, 1300, 1900, 3200, 4000, 4600, 4700, 4800, 4900, 5200, 5300, 5400, 6200, 6400, 6500, 6800, 7000, 7300, 7900, 8300, 8600]

Sorting the data

sorted_data = np.sort(data)

Calculating the position for the 74th percentile

k = 74 n = len(sorted_data) position = (k / 100) * (n + 1)

Interpolating to find the value at the 74th percentile

if position.is_integer(): p74 = sorted_data[int(position) - 1] # Exact index if position is an integer else: lower_idx = int(position) - 1 upper_idx = lower_idx + 1 p74 = sorted_data[lower_idx] + (position - lower_idx - 1) * (sorted_data[upper_idx] - sorted_data[lower_idx])

p74The 74th percentile (P74) for the given data is 6856.

If you'd like more details on the calculation process or have any further questions, feel free to ask!

Here are some related questions to explore:

1. How do you calculate other percentiles (e.g., P25 or P90)?
2. What is the difference between percentile and quartile?
3. How can we visualize percentiles in a box plot?
4. How do you handle ties in data when calculating percentiles?
5. What are some common uses of percentiles in data analysis?

Tip: Percentiles are useful in understanding the relative position of a value within a dataset, and they help in identifying outliers or trends in data.