# Salary one-quarter of the oldest employees were

Salary Analysis

Our goal is to analyze
salaries in a company based on a survey had happened among its employees. 378
employees took part in our survey. In the survey asked employees about the
following things:

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·
Age (in years)

·
Gender

·
Job seniority (in years)

·
Department (office,
production, sales)

·
Salary

We want to get some
information about distribution above variables and check which variables have
the greatest impact on salaries.

Gender

Let’s see gender
frequency distribution looks like in this company:

Man

240

Woman

138

More than half of the
company’s employees are men – our company is involved in the production of a
certain product, so employs many employees which working physically – hence a
large number of men in company.

Department

As it was mentioned at
the beginning, our company have three departments – office, production and
sales. Let’s see how many people work in each of them.

Office

24

Production

274

Sales

80

As we expected – the
vast majority of employees are production employees – around 70 percent of all
employees.

Age

The next variable that
was asked in the survey was the employee’s age. Let’s count the basic
statistics for this variable:

Statistic

Value

Number

378

Central tendency

Mean

40,1

Median

40

Mode

31

Measures of position

Minimum

23

Maximum

62

First quartile

33

Third quartile

47

Measures of variability

Range

39

Inter-quartile Range

7

Variance

77,97

Standard Deviation

8,83

Coefficient of variation

0,22

Quartile coefficient of dispersion

0,18

Skewness

0,27

Kurtosis

-0,65

The average age of the
employee was 40.1 years. Half of the employees were 40 years old or less and
the largest number of employees participating in the study was 31 years old.
The youngest was 23 years old, the oldest – 63 years old. One-fourth of the youngest
employees were aged 33 and under, one-quarter of the oldest employees were aged
40 and over.
Observed  values of the variable vary
around 8, 83 years of the average value, about 22%.
Skewness it is close to zero, so the age distribution can be considered as
symmetrical.
Negative kurtosis speaks of a larger dispersion of results compared to the
standard normal distribution.

Let’s look how it looks
box-plot of age:

As it was mentioned
earlier, the distribution of age can be considered symmetrical in relation to
the average.
Let’s look how it looks histogram of age:

Histogram shows a slight
right-sided asymmetry in the age distribution.

Job seniority

Let us now analyze the
employees’ seniority:

Statistic

Value

Number

378

Central tendency

Mean

11,2

Median

11

Mode

9

Measures of position

Minimum

0

Maximum

36

First
quartile

6

Third
quartile

15

Measures of variability

Range

36

Inter-quartile
Range

5

Variance

50,52

Standard
Deviation

7,11

Coefficient
of variation

0,63

Quartile
coefficient of dispersion

0,43

Skewness

0,73

Kurtosis

0,48

The average job
seniority of the employee was 11.2 years. Half of the employees work in the
company for 11 years and more, while the most employees work with them have
been working in the company for 9 years. Minimum of job seniority is 0, the
longest working employee has been working in the company for 36 years. Quarter
of employees work in the company for 6 years and shorter, quarter of employees
work in the company for 15 years and longer.
Observed  values of the variable vary
around 7,11 years of the average value, about 63%, therefore, the variability
of seniority is high.
The skewness is positive so the distribution of seniority is positive skew- the
mass of the distribution is concentrated on the left of the figure.
Positive kurtosis says that the distribution is leptokurtic – the distribution
is more concentrated than the standard normal distribution.

Box-plot:

Histogram:

As we can see – the
internship distribution at the company is right-angled, so the majority of
employees are inexperienced.

Salary

Let us now analyze the
employees’ salaries:

Statistic

Value

Number

378

Central tendency

Mean

3634,1

Median

3300

Mode

3400

Measures of position

Minimum

1700

Maximum

19500

First
quartile

2700

Third
quartile

3950

Measures of variability

Range

17800

Inter-quartile
Range

625

Variance

3146299,10

Standard
Deviation

1773,78

Coefficient
of variation

0,49

Quartile
coefficient of dispersion

0,19

Skewness

4,07

Kurtosis

25,60

The average salary in
this company was 3634,1 PLN. Half of employees earn 3300 and less, the most
people earn 3400. The person who earning the least earns 1700, the most –
19500. Quarter of employees earn 2700 or less, one fourth of the earners earn
the most earn 3950 and more.
Observed  values of the variable vary
around 1773,78 PLN of the average value, about 49%, therefore, so salaries are
moderately varied.

The skewness is strong
positive so the distribution of seniority is positive skew- employees with
below-average earnings prevail.

Strong positive kurtosis
says that the distribution is leptokurtic – the distribution is significantly
more concentrated than the standard normal distribution.

Box-plot:

Histogram:

On the charts you can
see what we wrote above – strong right-sided asymmetry of the distribution.

Correlation and regression

The only quantitative
variables in the study were age, seniority and salaries. We want to check
whether we are able to estimate salaries with the help of age or seniority. For
this purpose, let’s count the Pearson correlation coefficient between salaries
and age and seniority:

Pearson correlation coefficient with
Earnings

Age

Job seniority

0,405

0,413

We see that both age and
internship can explain the variability of earnings equally. So let’s build a
linear regression model where the dependent variable will be salaries (Y) and
an independent seniority (X).

As we can see the relationship
between salaries and seniority, we can describe the formula:

So, if seniority increases by one year,
the salary will increase by 103,19 PLN.
New person at work will get averagely 2473,3 PLN.
And for example – a person with 10 years of work experience should earn an
average 3505,2 PLN.

Seniority can explain the variability of
salaries in 17% – this is a weak dependency.

Estimation

We will try to perform
point and interval estimation for the salaries of employees.

Average

·
Point estimation

? = 3634,1 ± 91,2

·
Interval estimation –
level of confidence = 0,95

P(3455,3
< µ < 3812,9) = 0.95   Therefore, at 95% the average salaries in this company are in the range from 4716,6 to 5074,3.   Standard deviation   ·      Point estimation ? = 1773,78 ·      Interval estimation - level of confidence = 0,95 P(1655,71< ? < 1910,13) = 0.95   Therefore, at 95% standard deviation of salaries in this company are in the range from 1655,71 to 1910,13. Hypothesis Let's check whether women and men earn the same amount in this company: ?1  - woman salaries ?2  -man salaries     Woman Salaries Man Salaries Mean 3712,68 3588,96 Standard deviation 1832,00 1741,70 number of observations 138 240 Z 0,644 p-value 0,520   Therefore, at the significance level of 0.05, we can say that there is no reason to argue that men and women earn different amounts.

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