91Ó°ÊÓ

The mean is one of the most commonly used measures of central tendency. It is also known as the average. To calculate it, you sum all the data points and then divide by the number of data points.
In our exercise, the data points are: 60.5, 128.0, 84.6, 122.3, 78.9, 94.7, 85.9, and 89.9.
First, we add all the numbers:
\[60.5 + 128.0 + 84.6 + 122.3 + 78.9 + 94.7 + 85.9 + 89.9 = 745.8\]
Next, we divide by the number of data points, which is 8:
\[ \text{Mean} = \frac{745.8}{8} = 93.225 \]
This means that on average, students took about 93.225 minutes to complete the online portion of the exam. It's a useful summary because it gives an overall sense of the dataset.

The median is the middle value in a data set when it is arranged in ascending order. If there is an even number of data points, the median is the average of the two middle numbers.
First, let's sort the data in ascending order: \([60.5, 78.9, 84.6, 85.9, 89.9, 94.7, 122.3, 128.0] \)
Since we have eight values, we need to find the average of the fourth and fifth values. These values are: \(84.6\) and \(85.9\).
So, the median calculation is:
\[\text{Median} = \frac{84.6 + 85.9}{2} = \frac{170.5}{2} = 85.25\]
This tells us that half of the students took less than 85.25 minutes, and half took more. The median provides a good indication of the central point of the dataset, especially when the data is skewed.

The mode is the value that appears most frequently in a data set. It is possible to have more than one mode or no mode at all.
In our case, the data points are: \([60.5, 78.9, 84.6, 85.9, 89.9, 94.7, 122.3, 128.0] \).
Each value in the dataset is unique, meaning none of the values repeat.
Thus, there is no mode for this dataset.
The mode is particularly useful when you have data with many repeating values, and you want to understand which is the most common or popular.