The table below shows the wages of employees at the Yacht Club.

Question

a) Copy the table and complete the class centre column.

Hourly Class

Wage Centre. Frequency

14-18 44

19-23 35

24-28 13

29-33 8

b) How many employees are shown in the table?

c) What is the modal class?

d) Calculate an estimate of the mean wage.? I don't understand this one

Answer 1

Hi....

With the data that you provided, this is data from a HISTOGRAM.

To find the TOTAL number employees you will need to SUM up the FREQUENCIES, as the frequency values are how often the hourly rate values occur

So...TOTAL # of employees = ∑(frequencies) = 44 + 35 + 13 + 8 = 100

To determine the CLASS Centre, that is the MIDDLE or CENTER value of each group or HISTOGRAM bar, take each group and find the average or middle #

14 - 18 ... Class centre = (14 + 18)/2 = 16

19 - 23 ... Class centre = (19 + 23)/2 = 21

24 - 28 ... Class centre = 26

29 - 33 ... Class centre = 31

Lastly, you can ESTIMATE the MEAN AVERAGE of a HISTOGRAM by taking the CLASS Centre (or midpoint of each histogram bar) multiplying it by the FREQUENCY the corresponding frequency and dividing the FINAL TOTAL by the number of data points/employees. The same way you would find the MEAN if you were giving all of the data points. There is no way to calculate the ACTUAL mean from the histogram but this approach helps with an ESTIMATE of the AVERAGE MEAN

Estimated Average Mean = (16)(44) + (21)(35) + (26)(13) + (31)(8) / 100

Estimated Average Mean = (704 + 735 + 338 + 248) / 100

Estimated Average Mean = 20.25

Hope this helps :)

Answer 2

Hi,

b

The word frequency means how many .So, the first number 44 under the frequency column tell us that there are 44 employees who earn between $14 and $18, both numbers inclusive. So the total of the frequency column tells you the total number of employees shown in the table.

That is (44+35+13+8)= 100 employees.

We can represent this by ∑f_i where f_i represents how many wages/employees in the i^th class. For example, f₂ in this problem will be 35.

a

We will represent the class center by x_i. The class center is the average of the upper and lower limits for each class interval (Hourly Wage). For example the first number under x_i will be (14+18)/2=16.This is the class center for the first class. Let us make a new table as shown below

Hourly x_i f_i x_i•f_i

wage

14-18 16 44 704

19-23 21 35 735

24-28 26 13 338

29-33 31 8 248

c.

Modal class- Which class has the highest frequency?. You can see that the highest frequency is 44 for the class 14-18. So, the modal class is 14-18. This means, most of the employees have wages between 14 and 18 dollars.

d.

Estimate of the mean wage- Mean wage means the average wage. While we have 100 employees, this table does not tell us the wages for each of the 100 employees. So, it is only possible to estimate the mean wage. we cannot provide the accurate number for the mean wage.

To estimate the mean wage, we divide the total of the last column by the total number of employees.

"x -bar" (x with a line on top)= ∑(x_i •f_i)/∑f_i

_{= 2025/100}

_=20.25

_{The average wage is estimated to be $20.25.}

_{Please review Grouped Frequency Data and practice!}