Questions: Find the 16th percentile. The 16th percentile is 15.0 Alternate Answer: The 16th percentile is 15. Find the 80th percentile. The 80th percentile is

Solution Steps

The given dataset is sorted as follows: \[ \text{Sorted data} = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100] \]

To find the \(80^{\text{th}}\) percentile, we use the formula for the rank: \[ \text{Rank} = Q \times (N + 1) = 0.8 \times (10 + 1) = 8.8 \] where \(N\) is the number of data points.

Since the rank \(8.8\) is not an integer, we identify the lower and upper values:

• \(X_{\text{lower}} = 80\) (the value at rank 8)
• \(X_{\text{upper}} = 90\) (the value at rank 9)

We apply the averaging formula to find the \(80^{\text{th}}\) percentile: \[ Q = \frac{X_{\text{lower}} + X_{\text{upper}}}{2} = \frac{80 + 90}{2} = 85.0 \]

Final Answer