Suppose, we have 9 observations such that 48, 46, 21, 25, 103, 83, 88, 93, 112.Calculate 10th, 50th and 100th percentiles?

To calculate the 10th, 50th, and 100th percentiles of a data set, you first need to sort the data in ascending order.

The sorted data set is: 21, 25, 46, 48, 83, 88, 93, 103, 112.

1. To find the 10th percentile (P10), you use the formula P = 1 + (n - 1)*p, where n is the number of data points and p is the percentile in decimal form. For P10, p = 0.10. So, P = 1 + (9 - 1)0.10 = 1.8. Since this is not a whole number, we interpolate between the first and second data points. P10 = 21 + 0.8(25 - 21) = 24.2.

2. To find the 50th percentile (P50), also known as the median, you use the same formula. For P50, p = 0.50. So, P = 1 + (9 - 1)*0.50 = 5. This is a whole number, so the 5th data point is the 50th percentile. P50 = 83.

3. The 100th percentile (P100) is simply the highest data point in the set. So, P100 = 112.

So, the 10th, 50th, and 100th percentiles of the data set are 24.2, 83, and 112, respectively.