Question

Five students visiting the student health center for a free dental examination during National Dental Hygiene Month were asked how many months had passed since their last visit to a dentist. Their responses were: \(\begin{array}{lllll}6 & 17 & 11 & 22 & 29\end{array}\)

Short answer

The mean of the data set is given by \( \frac{6 + 17 + 11 + 22 + 29}{5} = 17 \), the median is 17, the range is \(29 - 6 = 23\), and there is no mode as all numbers are unique. Therefore, the mean is 17, the median is 17, the range is 23, and there is no mode.

Step-by-step solution

Calculate the Mean

The mean, or the average, is calculated by adding all numbers in the dataset and then dividing by the amount of numbers. Here, the numbers are 6, 17, 11, 22, and 29. Sum these numbers and divide by 5 (the total number of data points) to find the mean.

Determine the Median

Median is the middle value in an ordered set of values. First, we need to arrange the dataset from smallest to largest. Then, as we have 5 elements, the median is the third value (when counting from smallest to greatest). In case of an even number of elements, the median would be the average of the two middle numbers.

Find the Range

The range is the difference between the highest and the lowest value in the dataset. Identify the smallest (6) and the largest (29) numbers in the dataset, then subtract the smallest from the largest to find the range.

Identify the Mode

The mode is the number that appears most frequently in the dataset. If all numbers appear only once, the dataset has no mode. In this dataset, all numbers appear only once, so there is no mode.