Question

select the correct answer from each drop - down menu.
the data set gives the number of hours it took each of the 10 students in a cooking class to master a particular technique.
{5, 3, 5, 30, 4, 5, 4, 3, 4, 5}
the best measure of center for this data set is ↓, and its value is ↓.
(the drop - down options for the first blank are: first quartile, mean, median, range; the drop - down option for the second blank is 4.5)

Explanation:

Step1: Analyze the data set

The data set is {5, 3, 5, 30, 4, 5, 4, 3, 4, 5}. First, we check for outliers. The value 30 is much larger than the other values, so using the mean would be affected by this outlier. The median is a better measure of center for data with outliers.

Step2: Calculate the median

First, we sort the data set: {3, 4, 4, 4, 5, 5, 5, 5, 30}. Wait, wait, there are 10 data points. Let's sort correctly: 3, 4, 4, 4, 5, 5, 5, 5, 30? No, wait, the original data set has 10 elements: 3, 4, 4, 4, 5, 5, 5, 5, 30? Wait, no, let's list all 10: 3, 4, 4, 4, 5, 5, 5, 5, 30? Wait, no, the original data is {5, 3, 5, 30, 4, 5, 4, 3, 4, 5}. Let's sort them in ascending order: 3, 3, 4, 4, 4, 5, 5, 5, 5, 30. Now, for a data set with 10 (even) number of elements, the median is the average of the 5th and 6th values. The 5th value is 4 and the 6th value is 5. So the median is $\frac{4 + 5}{2} = 4.5$.

Step3: Determine the best measure

Since there is an outlier (30), the mean would be pulled up by the outlier. The median is not affected by outliers as much, so the best measure of center is the median, and its value is 4.5.

Answer:

The best measure of center for this data set is median, and its value is 4.5.