Video Transcript
The following table shows the
salaries 𝑠 of employees in a certain company, given in Egyptian pounds. Estimate the mean salary in
Egyptian pounds, giving your answer approximated to two decimal places.
The given table is a grouped
frequency table. The first column tells us that five
employees earned a salary greater than or equal to 1000 Egyptian pounds and less
than 3000 Egyptian pounds. The second column tells us that
eight employees earned a salary greater than or equal to 3000 Egyptian pounds and
less than 5000 Egyptian pounds. There were three employees and five
employees in the third and fourth groups, respectively. As we are not told the exact
salaries of any of the employees, we cannot determine the exact mean. Instead, we need to find an
estimate for the mean.
To do this, we follow a four-step
process, the first of which is to find the midpoint of each group, which we will
call 𝑥. To find the midpoint of each group,
we add the boundary values and divide by two. This means that in the first
column, we need to add 1000 and 3000 and then divide this answer by two. This is equal to 2000. So the midpoint of 1000 and 3000
Egyptian pounds is 2000 Egyptian pounds. Repeating this for the second
column, we see that the midpoint of 3000 and 5000 is 4000. Likewise, the midpoint of 5000 and
7000 is 6000, and the midpoint of 7000 and 9000 is 8000.
Our next step is to multiply the
midpoints by the frequencies 𝐹, which in this case is the number of employees in
each group. In the first column, we multiply
2000 by five and add the answer to the bottom row of our table, which we have
labeled 𝐹𝑥. 2000 multiplied by five is
10000. Next, we multiply 4000 by eight,
giving us 32000. 6000 multiplied by three is
18000. And finally, 8000 multiplied by
five is 40000.
Our next step is to find the total
of 𝐹, the number of employees, and the total of 𝐹𝑥. This is because the estimate for
the mean is calculated by dividing the total of 𝐹𝑥 by the total of 𝐹. The sum of five, eight, three, and
five is 21. Adding 10000, 32000, 18000, and
40000 gives us 100000. We can therefore calculate an
estimate for the mean by dividing 100000 by 21. This is equal to 4761.9047 and so
on. We are asked to give our answer to
two decimal places. And we can therefore conclude that
an estimate for the mean salary at the company in Egyptian pounds is 4761 pounds
90.
