Solving Word Problems with Median and Mean
We are often intimidated by questions that involve doing two types of data interpretation, especially if they are word problems.
Today we will discuss and learn how to approach a word problem that asks you to interpret information based off an average and then use that to help you make a decision regarding the median… this all sounds scary now, but I’ll walk you through it.
Let’s get started.
A company boasts that its mean starting salary is $61,000. Below is the list of the starting salaries on which the company based its claim. New Employee Starting Salary A $27,000; B $29,000 C $37,000; D $42,000 E $45,000; F $49,000 G $55,000; H $60,000 I $92,000; J $110,000 K $125,000 Determine what an astute job seeker should inquire about when presented with a mean starting salary figure.
Okay, as usual, let’s break down this word problem. It’s in two parts. Part one talks about how a company is saying it’s great because it’s mean (or average) starting salary is $61,000. What’s nice is the work is already done for us here, because it tells us the mean and then tells us all the wages. So, what are we supposed to do then? That’s part two.
The second part of this question tell us to figure out what someone should ask about given the average starting salary. This is tricky because it doesn’t explicitly tell us to do anything… it just tells us to find what question a job seeker should ask… it’s very broad. Let’s look at the data for a second. Do you notice anything about the different salaries, especially as they relate to the average of 61 thousand? Most of the salaries are lower than the average… by quite a bit.
What the creators of the problem want us to do then, is find out what question the job seeker should ask instead of “What’s your average salary?” What we should ask is what is the median salary. Remember, the median is the middle item in a set. In this case, we want to know what the middle salary is because the average is so deceiving. So, we see that we have 11 salaries, what’s the median? $49k. This is important to the job seeker because the median starting salary is a better indicator of the salary that can be expected, since this will not be inflated by salaries that are much larger or lower than the average. The median salary in this case is $49,000. This is likely to be closer to the starting salary of an average
I hope that helps, thanks for watching this video lesson. Until next time, happy studying.