Find the quartiles for the given dataset.
35, 40, 40, 45, 45, 50, 50, 50, 55, 60, 60, 65, 70
To find the quartiles for this dataset, we need to first put the numbers in order from smallest to largest:
35, 40, 40, 45, 45, 50, 50, 50, 55, 60, 60, 65, 70
There are 13 numbers in this dataset, so we can find the median (Q2) by taking the average of the middle two numbers. The middle two numbers are 50 and 50, so:
Q2 = (50 + 50)/2 = 50
To find Q1 (the first quartile), we need to find the median of the lower half of the dataset. The lower half of the dataset consists of the first six numbers:
35, 40, 40, 45, 45, 50
There are six numbers in this half of the dataset, so we can find the median by taking the average of the middle two numbers. The middle two numbers are 40 and 45, so:
Q1 = (40 + 45)/2 = 42.5
To find Q3 (the third quartile), we need to find the median of the upper half of the dataset. The upper half of the dataset consists of the last six numbers:
50, 50, 55, 60, 60, 65, 70
There are seven numbers in this half of the dataset, so we can find the median by taking the average of the middle two numbers. The middle two numbers are 60 and 60, so:
Q3 = (60 + 60)/2 = 60
Therefore, the quartiles for this dataset are Q1 = 42.5, Q2 = 50, and Q3 = 60.
To find the quartiles for the given dataset, we first need to sort the data in ascending order:
35, 40, 40, 45, 45, 50, 50, 50, 55, 60, 60, 65, 70
Step 1: Find the Median (Second Quartile, Q2)
The median is the middle value of the dataset. In this case, we have 13 data points, so the median will be the average of the 7th and 8th data points:
Median = (50 + 50) / 2 = 50
Step 2: Find the First Quartile (Q1)
The first quartile represents the lower 25% of the data. To find Q1, we need to find the median of the lower half of the data. In this case, the lower half of the data is:
35, 40, 40, 45, 45
Q1 = median of the lower half = (40 + 45) / 2 = 42.5
Step 3: Find the Third Quartile (Q3)
The third quartile represents the upper 25% of the data. To find Q3, we need to find the median of the upper half of the data. In this case, the upper half of the data is:
55, 60, 60, 65, 70
Q3 = median of the upper half = (60 + 60) / 2 = 60
So, the quartiles for the given dataset are:
Q1 = 42.5
Q2 = 50 (Median)
Q3 = 60