Question

In: Statistics and Probability

Suppose that it company employs 4 men and 4 women. Construct a hypothetical example which demonstrates...

Suppose that it company employs 4 men and 4 women. Construct a hypothetical example which demonstrates that even though the mean salary for men is much higher than the mean salary for women, it is possible for most of them women in the company to earn more than most of the men. List for hypothetical men salaries and for hypothetical women salaries for each to the following conditions hold the mean salary for men is higher than

the mean salary for women, and
3 of the 4 lowest salaries in the company belonged to men, and
3 of the 4 highest salaries and the company belonged to women.

A.Find the data set and verify that the 3 conditions are met.
B calculate the standard deviation of your data set using the TI. Explain each keystroke on the TI.
C discuss the reasons we prefer not to calculate standard deviation by hand in this course. Included vantages and disadvantages of each method ( by hand using formulas and using technology.)

Expert Solution

A. Suppose the dataset constructed is presented as follows:

Employee	Salary(in Rs.)
Man 1	70000
Woman 1	50050
Woman 2	50000
Woman 3	42000
Man 2	40500
Man 3	40100
Man 4	40000
Woman 4	30000

Here the dataset is such that the mean salary of the men employees is 47650 and that of the women is 43012.50. Hence the first condition is satisfied.

Secondly here the 4 lowest salaries are 30000,40000,40100,40500 out of which 3 belong to the men. Hence the second condition is satisfied.

Again here the 4 highest salaries are 70000,50050,50000,42000 out of which 3 belong to the women. Hence the third condition is satisfied.

B. Steps to calculate standard deviation in ti-84 plus.(IN CASE IF YOU NEED GUIDANCE FOR ANY OTHER MODEL OF THE CALCULATOR, YOU MAY COMMENT TO GET THE ANSWER)

Press the STAT button.
Go to EDIT option. Press the ENTER button.
Enter the data. Type the salaries one at a time and then press ENTER to make a record. You should have 8 observations in the L1 column.
Press the STAT button, then click on the right navigator to go to the CALC option. Select the 1-variable Stats and press ENTER.
Select the list as L1 (which is already done by default) and go to the Calculate option and then press ENTER.
A new window appears with various results displayed. As we have the full population here, here the standard deviation of the data is what is given by .

C. The advantages and disadvantages of standard deviation are listed as follows:

Advantages Of Standard Deviation:

1. Rigidly Defined: Standard deviation is rigidly defined measure and its value is always fixed.

2. Best Measure: Standard deviation is based on all the items in the series. So, it is the best measure of dispersion.

3. Less Affected: Standard deviation is least affected by the sampling fluctuations than other measures (mean deviation and quartile deviation).

4. Suitable For Algebraic Operation: Standard deviation can be used for mathematical operations and algebraic treatments. It is also applicable in statistical analysis.

Disadvantages Of Standard Deviation:

1. Complex Method: Standard deviation is complex to compute and difficult to understand as compared to other measures of dispersion.
2. High Effect: Standard deviation is highly affected by the extreme values in the series.

3. Standard deviation cannot be obtained for open end class frequency distribution.

4. It often becomes confusing whether to choose the value of S_X or as the appropriate value of the standard deviation.

Hopefully this will help you. In case of any query, do comment. Thanks

orchestra answered 2 years ago

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