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:
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
To find the quartiles for the given dataset:
Step 1: Sort the data in ascending order:
35, 40, 40, 45, 45, 50, 50, 50, 55, 60, 60, 65, 70
Step 2: Calculate the position of each quartile using the formula:
Position = (n + 1) * (k / 4)
Where n is the number of data points and k is the quartile number (1, 2, or 3).
Step 3: Calculate Q1 (the first quartile):
Position of Q1 = (13 + 1) * (1 / 4) = 14 * 0.25 = 3.5
Since the position is not a whole number, we take the average of the data points at positions 3 and 4:
Q1 = (40 + 40) / 2 = 40
Step 4: Calculate Q2 or the median (the second quartile):
Position of Q2 = (13 + 1) * (2 / 4) = 14 * 0.5 = 7
The data point at position 7 is 50.
Q2 or the median = 50
Step 5: Calculate Q3 (the third quartile):
Position of Q3 = (13 + 1) * (3 / 4) = 14 * 0.75 = 10.5
Again, the position is not a whole number, so we take the average of the data points at positions 10 and 11:
Q3 = (55 + 60) / 2 = 57.5
Final answer:
Q1: 40
Q2 or the median: 50
Q3: 57.5