To solve for the upper and lower quartiles of the given set of data, follow these steps:
1. List the Data in Ascending Order:
We first need to organize the dataset in ascending order. The data provided is:
```
92, 92, 95, 94, 80, 72
```
Sorting this data, we get:
```
72, 80, 92, 92, 94, 95
```
2. Identify the Lower Quartile (Q1):
The lower quartile, or Q1, is the median of the first half of the data. For a data set of 6 numbers, take the first three numbers:
```
72, 80, and 92
```
The median of this subset is the second number (since the data set is small and even-numbered, it’s straightforward):
```
Q1 = 80
```
3. Identify the Median (Not necessary but helps understand Q1 and Q3):
For completeness, the median itself (middle value) would be between the third and fourth numbers of the sorted list:
```
Median = (92 + 92) / 2 = 92
```
4. Identify the Upper Quartile (Q3):
The upper quartile, or Q3, is the median of the second half of the data. For our data set, the upper three numbers are:
```
92, 94, and 95
```
The median of this subset is the second number:
```
Q3 = 94
```
5. Conclusion:
The lower quartile (Q1) is [tex]\(80\)[/tex] and the upper quartile (Q3) is [tex]\(93.5\)[/tex].
Therefore, the correct option from the choices provided is:
- lower quartile: 80.5 upper quartile: 93
