SOLUTION: 1.The following salaries (in pesos) were obtained from a sample of 12 executive secretaries:
7,500 13,000 10,300 10,600 7,600 8,350
8,400 5,800 6,300 9,200 7,500 9,470
(a)Fi
Algebra.Com
Question 1201540: 1.The following salaries (in pesos) were obtained from a sample of 12 executive secretaries:
7,500 13,000 10,300 10,600 7,600 8,350
8,400 5,800 6,300 9,200 7,500 9,470
(a)Find estimates for the mean and variance of the salaries of all executive secretaries.
(b) What is the proportion of executive secretaries with salaries above P9,000.
Found 2 solutions by Glaviolette, math_tutor2020:
Answer by Glaviolette(140) (Show Source): You can put this solution on YOUR website!
Answer by math_tutor2020(3816) (Show Source): You can put this solution on YOUR website!
Answers:
(a) sample mean = 8668.33; sample variance = 3996669.70
(b) 0.416667
The decimal values are approximate.
Round however your teacher instructs.
================================================================================
Explanation for part (a)
The sample mean and sample variance estimate the population mean and population variance respectively.
Copy and paste the data into a spreadsheet.
I'm using Google Sheets, but the steps mentioned will work for excel, open office, libre office, etc.
The spreadsheet I made is linked at the bottom of this page.
I recommend reading this current solution page (a few times over) before visiting the spreadsheet link.
I'll have the input data start at cell A1 and stop at cell F2.
This input block has 2 rows and 6 columns.
In cell H1, type the command =AVERAGE(A1:F2) to compute the sample mean of the data values.
Don't forget about the equal sign up front. That is very important to be able to execute the command.
Otherwise, the spreadsheet treats it as plaintext only.
In cell H2, type =ROUND(H1,2) to round the number in cell H1 to 2 decimal places.
Replace the "2" with some other number to get a different level of precision.
The value 8668.33 should show up in cell H2.
Therefore, the sample mean is approximately 8668.33
Round however your teacher instructs.
Side note: another way to get the sample mean is to add up the values and divide by 12 (since there are 12 values).
Typing =SUM(A1:F2) will compute the sum, and that sum is 104020
So 104020/12 = 8668.3333 approximately
Now onto the sample variance.
In cell H4, type =STDEV(A1:F2) to compute the sample standard deviation of the data set.
Do not type STDEVP because that's the population version that is rarely used.
In cell H5, type =(H4)^2 which squares the previous result to get the sample variance.
Then finally for cell H6 we'll have =ROUND(H5,2) to round to 2 decimal places.
The result for cell H6 is 3996669.70 which is the approximate sample variance.
-----------------------------------------------
Explanation for part (b)
We need to count how many people in the sample have a salary over 9000 pesos.
We could do this by hand since the data set is fairly small, but let's use the spreadsheet to get practice for when the data set is much larger.
In cell H8, type =COUNTIF(A1:F2,">9000") to look through cells A1 to F2, and add to the count only if a salary is over 9000.
The result of cell H8 should be 5.
There are 5 people who have salaries over 9000 pesos.
How can we get the spreadsheet to highlight these 5 people?
In cell A4, type =IF(A1>9000,A1,"") and hit enter. The result will be blank. It's not a glitch or error. The command asks "is the stuff in A1 larger than 9000?".
If the answer is "yes" then it will display the contents of A1. Otherwise, it displays a blank empty string "".
Because the salary in A1 is 7500, it doesn't meet the criteria of being over 9000. So that's why cell A4 is blank. The quote marks aren't displayed in cell A4.
After the command is typed into A4, grab the very small marker at the bottom right corner of the cell. Drag it to cell F4.
Cells B4, C4, D4 will fill in with corresponding values from B1,C1,D1 to indicate the salaries (so far) that are over 9000 pesos.
Then drag down one row to fill the second row of values. There are two extra salaries in cells D5 and F5 that fill in with values over 9000.
The five salaries that get highlighted are:
13000,10300,10600,9200,9470
Conditional formatting is an alternative pathway to highlight these five salaries.
This process is handy to verify that the COUNTIF function is doing its job correctly.
Also you can visually inspect the original data set to make sure.
After all that we have 5 people out of 12 total who have salaries over 9000 pesos.
In cell H9, type in =5/12 and the result is approximately 0.416667; the 6's go on forever but of course we round at some point.
Therefore, roughly 41.67% of the sample has a salary over 9000 pesos.
Here is the link to the spreadsheet
https://docs.google.com/spreadsheets/d/1-p1VKWuGSrtLrpbKU0oGSfYwR4hO7ai_OlF087r9XXE/edit?usp=sharing
You don't need to have a google account, or to log in, to be able to access this spreadsheet.
You can save copy of the spreadsheet to your local machine (or to your google drive) so you can edit if needed.
Click on any cell to have its formula show up at the top (input bar).
RELATED QUESTIONS
H. LTD consolidated financial statement on 31 December 2020 was as follows;
Credit sales (answered by ikleyn)
The following information was obtained from the accounting records of Kamuka Traders for... (answered by ikleyn)
The average monthly sales of 5000 firms are normally distributed with mean Rs. 36,000 and (answered by Fombitz)
(i) When do you apply the analysis of variance technique?
(ii) The three samples given... (answered by CPhill)
Need help in Statistics?
1. What are some specific challenges related to creating a... (answered by lynnlo)
The following information was obtained from the accounting records of Nkomo Traders for... (answered by ikleyn)
6. All else being equal, as the sample size increases, the width of a 95% Confidence... (answered by Theo)
6.All else being equal, as the sample size increases, the width of a 95% Confidence... (answered by Boreal)
A hotel bill for N$ 840.00 is divided between 3 workers in the ratio of their salaries.... (answered by addingup)