Certainly! Let’s work through the problem step-by-step, considering the sample of 25 undergraduates' entertainment expenses provided.
### Given Data
The dollar amounts of entertainment expenses last year reported by undergraduates are:
684, 710, 688, 711, 722, 698, 723, 743, 738, 722, 696, 721, 685, 763, 681, 731, 736, 771, 693, 701, 737, 717, 752, 710, 697.
#### Step 1: Organize the data
First, let's sort the data in ascending order:
[tex]\[
681, 684, 685, 688, 693, 696, 697, 698, 701, 710, 710, 711, 717, 721, 722, 722, 723, 731, 736, 737, 738, 743, 752, 763, 771
\][/tex]
#### Step 2: Calculate the Mean
The mean is the average of the numbers. To calculate the mean, sum all the values and then divide by the total number of values.
[tex]\[
\text{Sum of expenses} = 681 + 684 + 685 + 688 + 693 + 696 + 697 + 698 + 701 + 710 + 710 + 711 + 717 + 721 + 722 + 722 + 723 + 731 + 736 + 737 + 738 + 743 + 752 + 763 + 771
\][/tex]
[tex]\[
= 17472
\][/tex]
The number of data points is 25.
[tex]\[
\text{Mean} = \frac{\text{Sum of expenses}}{\text{Number of data points}} = \frac{17472}{25} = 698.9
\][/tex]
#### Step 3: Calculate the Median
The median is the middle value when the data is arranged in order. Since there are 25 values (an odd number), the median is the 13th value.
Counting the 13th value in the sorted list:
[tex]\[
\text{Median} = \text{717}
\][/tex]
#### Step 4: Calculate the Mode
The mode is the number that appears most frequently in the data set.
From the sorted data, we can see that the value 710 and 722 both appear twice. All other values appear only once.
[tex]\[
\text{Mode} = 710, 722
\][/tex]
#### Conclusion
Here are your final values:
\begin{tabular}{|l|l|}
\hline
Mean & 698.9 \\
\hline
Median & 717 \\
\hline
Mode & 710, 722 \\
\hline
\end{tabular}
Note: Since mode 710 and 722 appear with the same frequency, there are two modes (bimodal).
