Final answer:
To find the 60th percentile of the data set 8, 32, 41, 56, 99, 120, we arrange the data in order, calculate the position using the formula (60/100) \(\times\) (N + 1), and then take a weighted average of the 4th and 5th values. The 60th percentile is 53.
Step-by-step explanation:
The student has asked how to find the 60th percentile of the following data set: 8, 56, 32, 41, 99, 120. To calculate the 60th percentile, we first need to order the data set from least to greatest and then determine the position in the dataset that corresponds to the 60th percentile. The position can be calculated using the formula: Position = (P/100) \(\times\) (N + 1) where P is the desired percentile and N is the number of data values in the set.
- First, we arrange the data: 8, 32, 41, 56, 99, 120.
- The number of data values, N, is 6.
- Calculate the position: Position = (60/100) \(\times\) (6 + 1) = 4.2.
- Since the position is not a whole number, we take a weighted average of the 4th and 5th values in the ordered dataset (41 and 56).
- To find this average: (0.2 \(\times\) 41) + (0.8 \(\times\) 56).
- The computation gives us: (8.2) + (44.8) = 53.
Therefore, the 60th percentile of the data set is 53.