Answer :
a. The 80th percentile is 33.3.
b. The 25th percentile is 13.1, and the 75th percentile is 34.7.
c. The median for these data is 16.6.
we need to arrange the data in ascending order:
2.1, 3.1, 7.4, 11.3, 12.1, 13.1, 13.3, 15.6, 16.6, 20.3, 23.2, 24.5, 25.9, 26.8, 28.5, 33.3, 34.7, 37.9, 37.9, 42.9
a. The formula to calculate the percentile position is (P / 100) * (n + 1), where P is the desired percentile (80 in this case) and n is the total number of data points (20 in this case).
(80 / 100) * (20 + 1) = 16.8.
Therefore, the 80th percentile is the 17th value in the ordered data set, which is 33.3.
b. To find the 25th and 75th percentiles, we can use the same process.
For the 25th percentile:
(25 / 100) * (20 + 1) = 5.25.
Rounding up to the next whole number, the 25th percentile is the 6th value in the ordered data set, which is 13.1.
For the 75th percentile:
(75 / 100) * (20 + 1) = 15.75.
Rounding up to the next whole number, the 75th percentile is the 16th value in the ordered data set, which is 34.7.
c. The median is the value that separates the lower half from the upper half of the ordered data set. Since we have an odd number of data points (20), the median will be the middle value.
The middle value is the 10th value in the ordered data set, which is 16.6.
Learn more about mean and median;
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