Question

6. The GPAs of fifteen random students are sorted from lowest to highest below: op lantai 11 5 6 7 8 9 | 10 11 12 13 15 9 Oll 2.0 T211 2.31 241 2.5AT 2 662 839 90 T311 313 3.16 | 3,421 367 395 | (a) Find the 33th percentile of this dataset. (b) Find the 80th percentile of this dataset.

Answer 1

a) Total Number of students (n) = 15

For calculating 33th percentile we need to multiply 33% by total number of students (i.e. 15 in this case).

= 33%*15 = 4.95 or 5 (rounded off to the nearest whole number)

Therefore the 33th percentile will be 5th GPA from the data arranged from lower to higher.(i.e. 2.41 in this case).

Hence the 33th percentile of this dataset is 2.41.

b)  For calculating 80th percentile we need to multiply 80% by total number of students (i.e. 15 in this case).

= 80%*15 = 12

As 12 is the exact whole number, we need to take average of GPA at 12th (i.e. 3.16) and 13th (i.e. 3.42) position for calculating 80th percentile which is calculated as follows:-

80th percentile = [(3.16+3.42)/2] = 3.29

Hence the 80th percentile of this dataset is 3.29.