a. The 40th percentile is 41.
b. The 78th percentile is 70.
To find percentiles, you first need to arrange the data in ascending order. Here are the ages in ascending order:
18, 21, 22, 25, 26, 27, 29, 30, 31, 33, 36, 37, 41, 42, 47, 52, 55, 57, 58, 62, 64, 67, 69, 71, 72, 73, 74, 76, 77
a. To find the 40th percentile:
Percentile = (P/100)×(n+1)
where P is the percentile (40 in this case), and n is the number of data points (29 in this case).
40% of 29+1=30 is 0.4×30=12.
The 12th value in the ordered list is 41. Therefore, the 40th percentile is 41.
b. To find the 78th percentile:
Percentile = (P/100)×(n+1)
78% of 29+1=30 is 0.78×30=23.4.
The 23.4th value is between the 23rd and 24th values. In this case, you can take the average of the 23rd and 24th values.
The 23rd value is 69, and the 24th value is 71.
Average of 69 and 71 is
=70.
Therefore, the 78th percentile is 70.