Explanation:
To find the quartile, decile, and percentile for the given dataset, we need to first organize the data in ascending order:
63.0, 63.4, 63.7, 64.2, 64.3, 69.1, 75.3, 81.6, 82.2, 82.9, 83.4, 84.2, 84.6, 84.6, 87.0
Now, we can use the following formulas to find the quartile, decile, and percentile:
Quartile: A quartile is a type of quantile that divides the dataset into four equal parts. To find the quartile, we can use the following formulas:
Q1 (first quartile): (n+1)/4th term
Q2 (second quartile or median): (n+1)/2nd term
Q3 (third quartile): 3(n+1)/4th term
Using the above formulas and the given data, we get:
Q1 = (15+1)/4 = 4th term = 64.3
Q2 = (15+1)/2 = 8th term = 81.6
Q3 = 3(15+1)/4 = 12th term = 84.2
Decile: A decile is a type of quantile that divides the dataset into ten equal parts. To find the decile, we can use the following formula:
D(n) = (n+1)/10th term, where n = 1, 2, ..., 9
Using the above formula and the given data, we get:
D1 = (15+1)/10 = 1.6th term = 63.4
D2 = 3.6th term = 64.2
D3 = 5.6th term = 69.1
D4 = 7.6th term = 81.6
D5 = 9.6th term = 82.9
D6 = 11.6th term = 84.2
D7 = 13.6th term = 84.6
D8 = 15.6th term = 87.0