Find the first and third quartiles of the following set of numbers.
13,4,12,16,8,14,8,3,10,8
Review the definition of quartiles. I will be happy to critique your work.
To find the first and third quartiles of a set of numbers, you need to arrange the numbers in ascending order. So let's first arrange the set of numbers in ascending order:
3, 4, 8, 8, 8, 10, 12, 13, 14, 16
Now, let's find the first quartile (Q1). The first quartile is the median of the lower half of the data set. Since the data set has 10 numbers, the lower half will consist of the first 5 numbers.
The median of the first 5 numbers (since it's an odd number of elements) is the middle number, which in this case is 8. So, Q1 = 8.
Next, let's find the third quartile (Q3). The third quartile is the median of the upper half of the data set. Again, since the data set has 10 numbers, the upper half will consist of the last 5 numbers.
The median of the last 5 numbers (since it's an odd number of elements) is the middle number, which in this case is 12. So, Q3 = 12.
Therefore, the first quartile (Q1) is 8 and the third quartile (Q3) is 12.