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 for the given dataset, we can follow these steps:
Step 1: Sort 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 the dataset has an odd number of values, the median is the middle value. In this case, the middle value is the 7th value: 50. Therefore, Q2 is 50.
Step 3: Find Q1:
Q1 is the median of the lower half of the dataset. In this case, the lower half consists of the values 35, 40, 40, 45, 45. We can find the median of this subset by taking the middle value, which is the 3rd value: 40. Therefore, Q1 is 40.
Step 4: Find Q3:
Q3 is the median of the upper half of the dataset. In this case, the upper half consists of the values 55, 60, 60, 65, 70. We can find the median of this subset by taking the middle value, which is the 3rd value: 60. Therefore, Q3 is 60.
So, the quartiles for the given dataset are:
Q1: 40
Q2 (median): 50
Q3: 60
To find the quartiles, we need to arrange the data in ascending order:
35, 40, 40, 45, 45, 50, 50, 50, 55, 60, 60, 65, 70
Q1 is the median of the lower half of the data. Since there are 13 numbers, the lower half has 6 numbers. The median of the lower half is the 3rd number in the lower half, which is 45.
Q2 or the median is the middle number of the dataset. Since there are 13 numbers, the median is the 7th number, which is 50.
Q3 is the median of the upper half of the data. Again, there are 13 numbers, so the upper half has 6 numbers. The median of the upper half is the 3rd number in the upper half, which is 60.
Therefore, the quartiles are:
Q1: 45
Q2 (median): 50
Q3: 60