Find the first and third quartiles, Q1 and Q3, of the following set of numbers. How do I do this when the numbers are:13, 4, 12, 16, 8, 14, 8, 3, 10, 8 and these are the answers that are given:A) 3; 16 B) 4; 14 C) 4; 12 D) 8; 13 Please help me.
Try different sites in here (most likely among the first 5 links) to learn how to determine quartiles:
http://www.google.com/search?q=finding+quartiles&rls=com.microsoft:en-us:IE-SearchBox&ie=UTF-8&oe=UTF-8&sourceid=ie7&rlz=1I7SUNA_en
If you give it a try and post your answer, a math tutor may come along later and let you know how you did.
To find the first and third quartiles, you need to follow these steps:
1. Arrange the data in ascending order:
3, 4, 8, 8, 8, 10, 12, 13, 14, 16
2. Calculate the position of the first quartile (Q1) using the formula:
Q1 = (n + 1) / 4
where n is the total number of data points.
In this case, n = 10, so:
Q1 = (10 + 1) / 4 = 11 / 4 = 2.75
This means that Q1 is between the second and third data points.
3. Find the value at the position of Q1:
Since the position is between the second and third data points, we average those two values:
Q1 = (4 + 8) / 2 = 12 / 2 = 6
So, Q1 is 6.
4. Calculate the position of the third quartile (Q3) using the formula:
Q3 = 3 * (n + 1) / 4
In this case:
Q3 = 3 * (10 + 1) / 4 = 33 / 4 = 8.25
This means that Q3 is between the eighth and ninth data points.
5. Find the value at the position of Q3:
Since the position is between the eighth and ninth data points, we average those two values:
Q3 = (12 + 13) / 2 = 25 / 2 = 12.5
So, Q3 is 12.5.
Comparing the calculated Q1 and Q3 values with the provided answer choices, we see that option C) 4; 12 matches with the calculated values.