find the first and third quartiles, Q1, and Q3, of the following numbers, 13,5,12,16,7,14,7,3,10,7
The first Q1 would be ( 1+n)4 = which is the 25 % of the data set
and the Q3 would be n(3)/4 = the 75 % of the data :
So for Q1 its :
n= 10
(1+11)/4 = 3
The 3 is not the q1, this just tells where at what position the number is so the thirds number in the data set is 12, so therefore Q1= 12
corrections first put the numbers is order:
And Q3 is (n+1)3/4
3,5,7,7,7,10,12,13,14,16,
SO Q1= 7
and Q3= 12(3)/4 = 9
So the 9th number is 14 therefore Q3= 14
I am still not understanding how you came up with the answer, can you explain how to do it Thanks
To find the first and third quartiles (Q1 and Q3) of a set of numbers, you need to follow these steps:
1. Arrange the numbers in ascending order: 3, 5, 7, 7, 7, 10, 12, 13, 14, 16.
2. Identify the position of Q1. Q1 is the median of the lower half of the data set. Since there are 10 numbers, Q1 will be the 25th percentile, which is located at position (25/100) * (10+1) = 2.75.
This means the position of Q1 is between the 2nd and 3rd numbers, which are 3 and 5. To find the exact value for Q1, you can use linear interpolation:
Q1 = 3 + (0.75 * (5-3)) = 3 + (0.75 * 2) = 3 + 1.5 = 4.5.
Therefore, Q1 is 4.5.
3. Identify the position of Q3. Q3 is the median of the upper half of the data set. Since there are 10 numbers, Q3 will be the 75th percentile, which is located at position (75/100) * (10+1) = 8.25.
This means the position of Q3 is between the 8th and 9th numbers, which are 13 and 14. To find the exact value for Q3, you can use linear interpolation:
Q3 = 13 + (0.25 * (14-13)) = 13 + (0.25 * 1) = 13 + 0.25 = 13.25.
Therefore, Q3 is 13.25.
So, the first quartile (Q1) is 4.5, and the third quartile (Q3) is 13.25.