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 first need to arrange the dataset in ascending order:
35, 40, 40, 45, 45, 50, 50, 50, 55, 60, 60, 65, 70
Next, we can find the median (Q2) of the dataset.
Q2: The median is the middle value of the dataset, which would be the 7th value when arranged in ascending order.
Therefore, Q2 = 50.
To find Q1 and Q3, we divide the dataset into two halves at the median:
First half: 35, 40, 40, 45, 45
Second half: 55, 60, 60, 65, 70
Now, we can find the median for each half.
Q1: The median of the first half would be the middle value, which is the 3rd value when arranged in ascending order.
Therefore, Q1 = 40.
Q3: The median of the second half would be the middle value, which is the 3rd value when arranged in ascending order.
Therefore, Q3 = 60.
So, the quartiles for the given dataset are:
Q1 = 40
Q2 or the median = 50
Q3 = 60
To find the quartiles for the given dataset, we need to arrange the data in ascending order first:
35, 40, 40, 45, 45, 50, 50, 50, 55, 60, 60, 65, 70
Step 1: Find the median (Q2)
Since there are an odd number of data points (13), the median is the middle value. In this case, the median is the 7th value, which is 50.
Q2 or the median: 50
Step 2: Find Q1 (the first quartile)
To find Q1, we need to find the median of the lower half of the data set. In this case, the lower half is the first 6 values:
35, 40, 40, 45, 45, 50
Again, there are an odd number of data points (6), so we find the middle value of the lower half, which is the 3rd value, 40.
Q1: 40
Step 3: Find Q3 (the third quartile)
To find Q3, we need to find the median of the upper half of the data set. In this case, the upper half is the last 6 values:
50, 50, 55, 60, 60, 65, 70
Just like before, there are an odd number of data points (7), so we find the middle value of the upper half, which is the 4th value, 60.
Q3: 60
Therefore, the quartiles for the given dataset are:
Q1: 40
Q2 or the median: 50
Q3: 60