Question content area top
Part 1
Find the quartiles for the set of numbers.
89, 70, 63, 91, 92, 96, 75, 87, 71, 74, 71
Question content area bottom
Part 1
The minimum is
enter your response here.
The minimum is 63.
whats the maximum
The maximum is 96.
whats the second quartile
To find the second quartile, also known as the median, we first need to arrange the numbers in ascending order:
63, 70, 71, 71, 74, 75, 87, 89, 91, 92, 96
There are 11 numbers in total, so the median is the middle value. In this case, the middle value is the 6th number when the numbers are in order:
Median = 75
So, the second quartile or median of the set of numbers is 75.
whats the first quartile
To find the first quartile, also known as Q1, we need to find the median of the lower half of the data set.
Given the data set arranged in ascending order:
63, 70, 71, 71, 74, 75, 87, 89, 91, 92, 96
We have a total of 11 numbers, which means the lower half has (11+1)/2 = 6 numbers. So, the first quartile is the median of the numbers below the overall median which is 75.
The lower half consists of: 63, 70, 71, 71, 74, 75
Calculating the median of the lower half, we find:
Q1 = (71 + 71)/2
Q1 = 71
Therefore, the first quartile Q1 of the data set is 71.
whats the thierd quartile
To find the third quartile, also known as Q3, we need to find the median of the upper half of the data set.
Given the data set arranged in ascending order:
63, 70, 71, 71, 74, 75, 87, 89, 91, 92, 96
We have a total of 11 numbers, which means the upper half has (11)/2 = 5 numbers. So, the third quartile is the median of the numbers above the overall median which is 75.
The upper half consists of: 87, 89, 91, 92, 96
Calculating the median of the upper half, we find:
Q3 = (91 + 92)/2
Q3 = 91.5
Therefore, the third quartile Q3 of the data set is 91.5.