Yasmine works as a server in a restaurant and earns different amounts in tips each night. Her earnings in tips over the course of 8 nights of work are shown in the following dataset. Find the mode of the dataset and explain whether the mode is descriptive of the dataset. { $10.45, $10.45, $35.80, $38.10, $40.90, $45.90, $79.60, $96.78 }.
The mode of a dataset is the value that appears most frequently. In this dataset, the value $10.45 appears twice, which is more frequent than any other value. Therefore, the mode of this dataset is $10.45.
While the mode gives us an idea of the most frequently occurring tip amount, in this case, $10.45, it may not be fully descriptive of the dataset. This is because there is a large range of tip amounts in the dataset, ranging from $10.45 to $96.78. The mode only tells us about the most common value but does not give us information about the spread or distribution of the other tip amounts. In this case, it might be more informative to also look at measures like the mean or median to get a better understanding of the average or central value of the dataset.