To calculate the lower quartile (Q1), median (Q2), and upper quartile (Q3) of the given dataset, we first need to arrange the data in ascending order. Here is the data set you provided:
3, 3, 4, 6, 6, 7
Now, let's organize the data:
3, 3, 4, 6, 6, 7
Step 1: Find the Median (Q2)
The median is the middle value of the dataset. If there is an even number of observations, the median is the average of the two middle numbers.
- The dataset has 6 elements (even number).
- The two middle elements are the 3rd and 4th values: 4 and 6.
\[ \text{Median} = \frac{4 + 6}{2} = \frac{10}{2} = 5 \]
Step 2: Find the Lower Quartile (Q1)
The lower quartile (Q1) is the median of the first half of the data (which is lower than the median).
The first half of our data is:
3, 3, 4
- The median of this subset (Q1) is the second value in this ordered subset:
- The second value here is 3.
\[ \text{Lower Quartile} (Q1) = 3 \]
Step 3: Find the Upper Quartile (Q3)
The upper quartile (Q3) is the median of the second half of the data (which is higher than the median).
The second half of our data is:
6, 6, 7
- The median of this subset (Q3) is the second value in this ordered subset:
- The second value here is 6.
\[ \text{Upper Quartile} (Q3) = 6 \]
Summary of results:
- Lower Quartile (Q1) = 3
- Median (Q2) = 5
- Upper Quartile (Q3) = 6
So, the final answers are:
- Lower Quartile (Q1) = 3
- Median (Q2) = 5
- Upper Quartile (Q3) = 6