Questions: Calculate the 60th percentile of the data shown x 3 3.2 6.2 12.3 17.9 18.2 18.3 27 28.1 29.2

Solution Steps

The given data points are sorted as follows: \[ \text{Sorted data} = [3, 3.2, 6.2, 12.3, 17.9, 18.2, 18.3, 27, 28.1, 29.2] \]

To find the 60th percentile, we use the formula for the rank: \[ \text{Rank} = Q \times (N + 1) = 0.6 \times (10 + 1) = 6.6 \] where \( Q \) is the desired quantile (0.6 for the 60th percentile) and \( N \) is the number of data points (10).

The rank of 6.6 indicates that we need to average the values at positions 6 and 7 in the sorted data:

• \( X_{\text{lower}} = 18.2 \) (6th position)
• \( X_{\text{upper}} = 18.3 \) (7th position)

Using the averaging formula: \[ Q = \frac{X_{\text{lower}} + X_{\text{upper}}}{2} = \frac{18.2 + 18.3}{2} = 18.25 \]

Final Answer