money and finances
In todays’ society, we are often met with “averages” when it comes to discussing things such as pay rates, annual salaries of different job positions, or other transactions that involve money and finances. However, the term “average” does not truly explain the real value of anything since we do not know whether it is the average of mode, median, or mean. For example, in a range of numbers involving 1-10, the median average would be 5. After adding up the sum of digits 1-10, we find that the mean average is 5.5. Lastly, the average mode would include the digit between the duplicate numbers that occur the most amount of times and duplicate numbers that occur the least amount of times. As you can see, there are three different “averages” that can be depicted from the same range of numbers, making it uncertain for one to know which average they are referring to. Furthermore, an average of a set of numbers only show one value, making it entirely possible for much of a set of numbers to be below the average.
When I was job searching a few years ago, I liked to search up the “average” annual salary from websites or magazines. Seeing a number such as $80,000 made the job position seem very appealing, and encouraged me to continue pursuing a career in that field. Upon applying for the position, I noticed that companies were only offering an annual salary of $60,000– $20,000 less than what I was expecting to make on “average.” As explained above, it became apparent later on that I had missed the point of an average. I had no idea whether it was the average of all the incomes for this position combined in the U.S. (mean), the median of what most individuals are paid, or whether it was the amount most people were likely to be paid. As such, I also had forgotten that having an average meant that I could be making either less than or more than the average annual salary—which in this case, was less.
1. Introduce key vocabulary: mean, median, mode, and range.
2. Tell a story to the class in order to make the lesson interactive and engaging. For example:
· Southern California needs your help! Dr. Nye, a scientist, has been researching the effects of weather temperatures in hopes of being able to predict temperatures for the future. However, California has been experiencing a range of temperatures from 60 degrees to 105 degrees over the past week! The plants are dying, and people are getting sick from constant change from hot to cold. Take a look at the temperatures in the past week to help predict the temperature for the next week.
3. In order to solve this problem, the first step is to help the residents of Southern California to sort the temperatures from least to greatest.
· [Come up with a range of numbers]
4. Questions to ask:
· Highest temperature this week?
· Lowest temperature this week?
· Middle temperature this week? (Median)
· Temperature that occurs the most frequently? (Mode)
· Difference between the highest and lowest temperature (Range)
i. Are patterns large or small based off of the range?
· What is the average temperature in Southern California based off of these numbers? (Mean)
5. For more interaction, ask students to come up and explain how they got their answer for mode, median, and mean.