Calculate the first, second, and third quartiles of the following sample.
2 2 3 3 4 4 4 5 5 5 7 7 8 9 10
Are my answers correct:
25th percentile = 3
50th percentile - 5
75th percentile = 7
In terms of whole numbers, you are right.
To calculate the quartiles of a sample, you need to order the data set in ascending order and then find the appropriate values. Here's how you can calculate each quartile:
Step 1: Sort the data in ascending order:
2 2 3 3 4 4 4 5 5 5 7 7 8 9 10
Step 2: Calculate the position of each quartile:
- The first quartile (25th percentile) is at the 25% of the way through the sorted data.
- The second quartile (50th percentile) is the median of the sorted data.
- The third quartile (75th percentile) is at the 75% of the way through the sorted data.
Step 3: Calculate each quartile:
- First Quartile (Q1):
To find the 25th percentile, multiply the position with (n+1)/100, where n is the total number of data points.
25th percentile position = (25/100) * (14+1)
25th percentile position = 3.75
Since the position is not a whole number, you can take the average of the 3rd and 4th value in the sorted data to find Q1.
Q1 = (3+3)/2
Q1 = 3
- Second Quartile (Q2/Median):
The second quartile is the median of the sorted data, which is the middle value.
Q2 = 4 (as it is the middle value)
- Third Quartile (Q3):
To find the 75th percentile, multiply the position with (n+1)/100, where n is the total number of data points.
75th percentile position = (75/100) * (14+1)
75th percentile position = 11.25
Since the position is not a whole number, you can take the average of the 11th and 12th value in the sorted data to find Q3.
Q3 = (7+7)/2
Q3 = 7
Therefore, the correct answers are:
Q1 = 3
Q2 = 4
Q3 = 7