116k views
2 votes
Find the quartile,decile,percentile for the following dataset, consisting of the midterm percentage ratings of n=15 students in an Grade 10 Math course: 82.9, 84.2, 81.6, 64.3, 69.1, 64.2, 82.2, 63, 83.4, 63.4, 87, 84.6, 84.6, 75.3, 63.7.

User Don H
by
7.8k points

1 Answer

4 votes

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

User Solvemon
by
8.7k points