Video Transcript
The following figure shows the
cumulative frequency graph for the monthly salary of employees in a company. Given that no employees have a
salary higher than 4,000 dollars, find the number of employees who have a salary
higher than 2,500 dollars.
In this question, we are given a
cumulative frequency graph of the monthly salary of employees at a company. We can recall that in a cumulative
frequency graph, we find the sum of all the previous frequencies up to that
point. So, in this case, the 𝑥-coordinate
of a point on the graph tells us the salary, and the corresponding 𝑦-coordinate
tells us the total number of employees who make less than or equal to that amount
monthly.
We want to use the given graph to
find the total number of employees who earn more than 2,500 dollars. And to do this, we are told that no
employee makes more than 4,000 dollars a month, which we note is the last value in
the horizontal axis of the graph. This means that all of the
employees are represented in the cumulative frequency graph.
We want to find the number of
employees at the company who earn more than 2,500 dollars a month. So we start by finding the point on
the graph with an 𝑥-coordinate of 2,500. We see that this is the point
2,500, 51. Remember, in a cumulative frequency
graph, this tells us the total frequency up to 2,500. So, this tells us that 51 of the
employees at the company earn 2,500 dollars a month or less.
We can also note that all of the
other employees must make more money than this. To determine the number of
employees who make more money than this, we need the total number of employees at
the company. We can find this using the graph by
recalling that no employee makes more than 4,000 dollars a month. So the cumulative frequency up to
this value includes all of the employees. Hence, there are 70 total employees
at the company.
Finally, if we subtract the 51
employees who earn less than or equal to 2,500 dollars a month from the 70 total
employees, we find that 19 employees earn more than 2,500 dollars a month.
