Find the quartiles for the given dataset.

Question

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 need to first arrange the data in ascending order:

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

Q1 is the lower quartile and represents the value below which 25% of the data falls. To find Q1, we need to find the median of the lower half of the data set. In this case, the lower half is:

35, 40, 40, 45, 45

The median of this lower half is the average of the two middle numbers, which are 40 and 45. So, Q1 = (40 + 45) / 2 = 42.5

Q2 or the median is the value that separates the lower half and the upper half of the data set. In this case, Q2 = 50.

Q3 is the upper quartile and represents the value below which 75% of the data falls. To find Q3, we need to find the median of the upper half of the data set. In this case, the upper half is:

55, 60, 60, 65, 70

The median of this upper half is the average of the two middle numbers, which are 60 and 65. So, Q3 = (60 + 65) / 2 = 62.5

Therefore, the quartiles for the given dataset are:

Q1: 42.5
Q2: 50
Q3: 62.5