Problem of the Week
Problem A and Solution
Healthy Eating
Problem
Ms. Morgan’s health class is discussing healthy eating choices. She asked 9 of her students to write down how many servings of fruits or vegetables they eat every day. The following chart shows the results.
| Student’s Name | Number of Servings |
|---|---|
| Vlad | 3 |
| Tessa | 2 |
| Shaheed | 4 |
| Maja | 2 |
| Mike | 3 |
| Braydon | 2 |
| Priya | 6 |
| Juan | 2 |
| Layla | 3 |
Given this data, what is the median (the number in the middle of the data when arranged in order) and the mode (the most common number) for the number of servings of fruits or vegetables consumed in a day by these students in Ms. Morgan’s health class?
Solution
One way to solve this problem is to list the numbers of servings in sorted order:
\[2, 2, 2, 2, (3), 3, 3, 4, 6\]
Since there are 9 data values, then the middle number is the 5th value of the sorted list. In the list above we have circled the middle number. So the median of the data is 3.
Also, the number that appears most often is 2. So 2 is the mode of the data.
Teacher’s Notes
Students may ask, “What is the average on a test?”, so they can judge how their own grade is measured against other students’ results. When they ask that question, they probably are asking about the mean value of the set of test marks. The mean is calculated by adding the numbers in the set of data together and dividing the sum by the size of the set. The mean of a set can be strongly influenced by extreme data values, so some would argue that the median is a better point of comparison.
For example, if the marks the class were: \(70, 72, 73, 75, 100\), then the mean would be \((70 + 72 + 73 + 75 + 100) \div 5 = 78\). In this case, four marks appear “below average”, whereas if we compare the results to the median (73), now only two marks are “below average” and most marks are close to the average. With this data set, the median probably describes the overall results of the class better than the mean.
There are two cases to consider when calculating the median of a set of numbers. When there are an odd number of values in the data set, when the data is arranged in order the middle number is the median. When there an even number of values in the data set, the mean of the two middle numbers is the median value.