Question

find the quartiles for the given dataset.

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

(2 points)

Answer 1

To find the quartiles for the dataset, we first need to determine the median (Q2) and then find the medians of the lower and upper halves to get Q1 and Q3.

Step 1: Arrange the data in ascending order:
35, 40, 40, 45, 45, 50, 50, 50, 55, 60, 60, 65, 70

Step 2: Find the median (Q2):
Since there are 13 numbers, the median is the average of the middle two numbers:
Median = (50 + 50) / 2 = 50

Step 3: Find the medians of the lower and upper halves to get Q1 and Q3:
Lower half (first 6 numbers) = 35, 40, 40, 45, 45, 50
Upper half (last 6 numbers) = 55, 60, 60, 65, 70

Q1 = Median of lower half = (40 + 45) / 2 = 42.5
Q3 = Median of upper half = (60 + 60) / 2 = 60

Therefore, the quartiles for the given dataset are:
Q1 = 42.5
Q2 = 50 (median)
Q3 = 60