Helping Your Child Understand the Difference Between Median, Mean, and Range
Posted on June 19th, 2019 2:07pm
In 2017, The Globe and Mail made waves by publishing a story reporting that half of all Grade 6 students in Ontario failed to meet provincial math standards as measured by the Education Quality and Accountability Office. These statistics showed a general decrease in math literacy across a range of different cohorts, and confirmed what many parents and educators already feared: that today’s children are falling behind when it comes to basic skills.
While it is hard to ascribe any single cause to such a notable dip in education outcomes, it is clear that the students of today are suffering from cuts to education and an increasingly sharp divide between schools that have adequate resources and those that don’t.
When you factor in the challenges many students already deal with when it comes to mastering the math curriculum (math anxiety is a problem that continues to affect a significant percentage of students), it is perhaps unsurprising that performance in math is starting to slip.
And while there are things you can do if you want to know how to overcome math anxiety or help your child engage with the math curriculum in more productive ways, improving your child’s math skills requires more than just exposure therapy: it requires intense one-on-one support that can help get your math questions answered so your child can learn to apply basic arithmetical concepts.
Tips for Teaching Median, Mean, and Range
One particular concept younger children are most likely to struggle with is the difference between median, mean, and range. One of the expectations set up by the Ontario math curriculum is that by the end of Grade 5, students will be able to calculate the mean, and understand how it relates to the median and range of a set of numbers. Not only is this a key part of the Grade 5 curriculum, it also features on the Grade 6 EQAO assessment of reading, writing, and mathematics.
Helping your child understand what these terms mean and how to apply them to problem solving is essential for their academic success, so if you they are having a hard time grasping these concepts, here are a few ways you can help them understand the difference between them.
For most of us, the concept of the mean, or “average,” is so familiar that it needs little explaining. But the concept of the mean isn’t nearly as intuitive for children, and helping them learn not just how to calculate the mean, but to understand the underlying principle, can take some work.
For example, if you have a set of six numbers (8, 12, 16, 14, 19, 7), you calculate the mean by adding these numbers up and then dividing by six. This will give you the average of the six values, 12.66. Children are often confused by the fact that this number is not part of the original set, which is why it is important, when teaching the mean, to stress that the average may be a seventh number that doesn’t appear in the original set of six.
In some ways, the median is easier to understand, as it takes fewer steps to arrive at the median than to calculate the mean. The median is simply the middle value in a sorted list of numbers, so to find the median all you need to do is arrange the numbers in order from smallest to greatest, add up the total number of numbers, and count up to find the middle number.
The challenge when teaching median is often more about helping kids focus in school than it is about particular difficulties with understanding the topic. It is common for children to confuse mean with median simply because the sound similar, so remind you child that the mean is the “mean old average” while the median is the mid-point.
Simply put, the range of a set of numbers is the difference between the highest number and the lowest, and can be found by putting the numbers in order and subtracting the smallest value from the greatest.
When teaching the range, it is often easiest to compare it to a “window.” The numbers in the range are what you can see out of the window, and the range is the size of the window.
The Role of Tutoring in Improving Competence in Arithmetic
Concepts like mean, median, and range are foundational tools for understanding mathematics, and if your child is going to be able to keep apace with their curriculum, they will need to be able to master them early on.
Unfortunately, the most effective way to lock these concepts into long-term memory is by repeated exposure. While math tends to be a skill that relies heavily on logical thinking, understanding the terminology of math is a matter of memorization, and tutors can play a helpful role in providing your child with extra help in fully understanding the ideas behind mean, median, and range.
Because tutoring allows children to encounter concepts on their own terms, without the fear of looking foolish for getting a question wrong, it can play an important role in helping children come to grips with difficult material. And if you learn about our educational philosophy you will know that we encourage our tutors to see themselves as smart friends coming alongside students to help them learn at their own pace and in their own way.
Math is one of those skills that your child is going to use every day of their life, and basic numeracy is as important as literacy in terms of helping your child land a good job. Students who excel at math have a head start in the job market, and according to one study undertaken by researches at Vanderbilt University’s Peabody School, mastery of arithmetical concepts early on is a major predictor of success later in life.
If you want to make sure your child is able to buck the trend of declining math scores, call Prep Academy Tutors today to make sure they have the support needed to master their curriculum.