determining mean... help?

#1
Im looking for the mean wage per employee per hour.

info is as follows.

hourly wage numbr of employees

$4.-4.50 255
$4.51-$5.50 345
$5.51-$7.50 625
$7.51- and above 275
-------
1500


there was other info in the problem but i THINK it was added to
confuse or smoke screen. What doyou think?

Last year the company had $395.50 in sales, cost of goods sold was $900,000,
annual payroll was $12,480,000. The company operated 52 weeks last year at standard work week of 40 hours. The researcher is overcome by the amountof data collected and now needs to dtermine the mean average wageper employee per hour.

Would you use the weighted mean?

i came up with

255(4.25)+345(5.)+ etc/ 1500

and came up with

$6.23

any thoughts?
 

JohnM

TS Contributor
#4
You could get a decent estimate using the table if it weren't for this:

"$7.51- and above" 275

It's difficult to assign a value for this "range" because there is no upper bound.

The best way here is to take the total payroll of $12,480,000 and divide by the employee count of 255+345+625+275 = 1500

annual: 12,480,000 / 1500 = 8320
hourly: 8320 / (40*52) = 4.00

but unfortunately this doesn't look right, considering the table given in the problem.
 
#5
$4.00 can't be right, as it is the lowest wage. I posed this problem to a friend of mine, and he concluded that the information given was insufficient and therefore the mean wage can not be determined. What do you think:confused:
 

ssd

New Member
#6
The information is sufficient. Use the frequency (or number) of employees falling in each catagory of pay range as weights. Then, you can find the avarage payment/employee/hour just by calculating the weighted avarage using the class mid points. All other information given are useless including the annual payroll. For the above 7.51 information, you have to form a class of length equal to that of the preceeding class.
Mean= (4.25*255+5.005*345+6.505*625+8.505*275)/1500 =6.143
Pls check the calculations yourself.

Donot confuse with the fact that all the 1500 employees did not work for 52 weeks and 40 hour a week. The annual pay role comes in to play if avarage payment (which is different than mean wage) per employee/hour over the year is asked for. This value is 4.00 as calculated by John M.
 
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