Let's analyze Francine's data set to determine which characteristic of the measurements matches the value of \(20.73 \, \text{g}\).
The measurements are:
- 20.73
- 20.76
- 20.68
- 20.75
### 1. Mean
The mean (or average) is calculated by summing all the values and then dividing by the number of observations.
[tex]\[
\text{Mean} = \frac{\text{Sum of all measurements}}{\text{Number of measurements}}
\][/tex]
Calculating the sum:
[tex]\[
20.73 + 20.76 + 20.68 + 20.75 = 82.92
\][/tex]
There are 4 measurements. So,
[tex]\[
\text{Mean} = \frac{82.92}{4} = 20.73
\][/tex]
### 2. Median
The median is the middle value of a data set that has been arranged in ascending order. If there is an even number of observations, the median is the average of the two middle numbers.
Arranging the numbers in ascending order:
[tex]\[
20.68, 20.73, 20.75, 20.76
\][/tex]
Since there is an even number of observations, the median is:
[tex]\[
\text{Median} = \frac{20.73 + 20.75}{2} = \frac{41.48}{2} = 20.74
\][/tex]
### 3. Mode
The mode is the value that appears most frequently in a data set.
In this data set, each measurement occurs exactly once. So, there is no mode for this data set.
### 4. Range
The range is the difference between the maximum and minimum values in the data set.
Maximum value = 20.76
Minimum value = 20.68
[tex]\[
\text{Range} = 20.76 - 20.68 = 0.08
\][/tex]
### Conclusion
Since Francine calculated a value of [tex]\(20.73 \, \text{g}\)[/tex], and this matches the mean calculated above, Francine has calculated the mean of the data set.
