Question

Find the quartiles for the given dataset.
35, 40, 40, 45, 45, 50, 50, 50, 55, 60, 60, 65, 70
(2 points)
Q1:
Q2 or the median:
Q3

Answer 1

To find the quartiles, we first need to arrange the data in ascending order:

35, 40, 40, 45, 45, 50, 50, 50, 55, 60, 60, 65, 70

Q1 (25th percentile):
Since there are 13 data points, the position of Q1 is (13+1)/4 = 3.5. This means that Q1 is the average of the 3rd and 4th data points.
Q1 = (40 + 40)/2 = 40

Q2 or the median (50th percentile):
Since there are 13 data points, the position of Q2 is (13+1)/2 = 7th data point.
Q2 = 50

Q3 (75th percentile):
Since there are 13 data points, the position of Q3 is 3*(13+1)/4 = 10th data point.
Q3 = 55

Therefore, the quartiles for the given dataset are:
Q1: 40
Q2: 50
Q3: 55