Question
10,11,13,18,1921,22,25,27,30,32
which is the lower quartile
which is the upper quertile
which is the lower quartile
which is the upper quertile
Answers
GPT-4o mini
To find the lower quartile (Q1) and the upper quartile (Q3) of the given data set, we first need to arrange the numbers in ascending order (which they already appear to be) and then determine their positions.
The data set is:
10, 11, 13, 18, 19, 21, 22, 25, 27, 30, 32
There are 11 data points in total.
### Step 1: Find the Lower Quartile (Q1)
Q1 is the median of the first half of the data (the lower 50%). For 11 data points, the first half includes the first 5 values:
10, 11, 13, 18, 19
To find Q1:
- This group has 5 values, so the median is the 3rd value.
- Q1 = 13.
### Step 2: Find the Upper Quartile (Q3)
Q3 is the median of the second half of the data (the upper 50%). For the data set, the second half includes:
21, 22, 25, 27, 30, 32
To find Q3:
- This group also has 6 values, so the median is the average of the 3rd and 4th values:
- Q3 = (25 + 27) / 2 = 26.
### Summary:
- Lower Quartile (Q1) = 13
- Upper Quartile (Q3) = 26
The data set is:
10, 11, 13, 18, 19, 21, 22, 25, 27, 30, 32
There are 11 data points in total.
### Step 1: Find the Lower Quartile (Q1)
Q1 is the median of the first half of the data (the lower 50%). For 11 data points, the first half includes the first 5 values:
10, 11, 13, 18, 19
To find Q1:
- This group has 5 values, so the median is the 3rd value.
- Q1 = 13.
### Step 2: Find the Upper Quartile (Q3)
Q3 is the median of the second half of the data (the upper 50%). For the data set, the second half includes:
21, 22, 25, 27, 30, 32
To find Q3:
- This group also has 6 values, so the median is the average of the 3rd and 4th values:
- Q3 = (25 + 27) / 2 = 26.
### Summary:
- Lower Quartile (Q1) = 13
- Upper Quartile (Q3) = 26