Final answer:
To calculate specific percentiles for the ages of male actors, one multiplies the desired percentile by the number of observations, rounds up to the nearest whole number, and identifies the age at that position in the ordered list. For instance, the 20th percentile is 27, and the 55th percentile is 52.
Step-by-step explanation:
To analyze the ages of recent award-winning male actors, we look at a list of ages and calculate specific percentiles. A percentile indicates the value below which a certain percentage of observations fall. For example, to calculate the 20th and 55th percentiles from a list of 29 ages ordered from smallest to largest, we follow this process:
- Multiply the percentile you want to find by the total number of observations (e.g., for the 20th percentile, 0.20 x 29 = 5.8).
- If the result is not a whole number, round up to the nearest whole number to determine the position of the percentile in the ordered list (e.g., round up to 6 for the 20th percentile).
- Find the value in that position of the ordered list (for the 20th percentile, the 6th value is 27).
Using the same approach for the 55th percentile, we get:
- Multiply 0.55 by 29 to get 15.95.
- Round up to 16 to get the position of the 55th percentile.
- The 16th value in the list is 52, which represents the 55th percentile.
Therefore, 27 is the 20th percentile, and 52 is the 55th percentile for the ages of award-winning best male actors.