Descriptive Statistics in Business Statistics

This article discusses the importance of skilled manpower and intellectual capital in the business world and how HR practices and policies can enhance employee satisfaction. It focuses on the use of descriptive statistics to analyze employee satisfaction levels before and after training, as well as the impact of gender and age on satisfaction. The article provides examples and recommendations based on the analysis.

BUSINESS STATISTICS
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Introduction
A key source of competitive advantage in the modern business world is skilled manpower
and intellectual capital. This is apparent from a growing trend where HR practices and
policies are given more attention so as to enhance the overall satisfaction level of employees.
In order to increase the job satisfaction, training is a useful measure as it improves the
employee skills and therefore tends to improve the job performance and associated
satisfaction. For testing the employee satisfaction, a survey has been conducted by the
company using employee sample. To understand the usefulness of training, the satisfaction
scores before and after the training have been measured. Additionally, the employee related
demographic variables also have been indicated which have been used for analysing any
particular relation or trend with regards to satisfaction while deploying descriptive statistics.
Definition of Problem
Currently, the main issue or problem that the company faces is lowering satisfaction levels of
employees. With this intent, the survey has been conducted to determine whether training has
led to any increase in satisfaction level. The company also intends to ascertain if the job
satisfaction tends to differ by gender which would enable the company to modify the policies
accordingly and also address gender specific concerns.
Also, there is use of descriptive statistical techniques so as to present a data summary which
would be useful for making relevant conclusions. This involves representation of the
variables in the form of tables and graphs so as to allow easy interpretation by the user.
Besides, the key characteristics of the underlying variables have been captured using the
requisite measures of location and variation depending on the nature of the underlying
variable. The prominent measures of location include mean, median mode while that of
variation include range, standard deviation, variance, coefficient of variation and IQR.

Definition of data variables
The requisite information about the data variables is summarised in the following table
(Flick, 2015).
Descriptive Statistics (Measures of Location)
In relation to provide summary of a survey data, one of the key parameters is the measures
associated with location or central tendency. In relation to the numerical variables, measures
of location are well defined and can be easily calculated. These include the following (Hair
et. al., 2015).
 Mean
 Median
 Mode
 Quartiles
It is imperative to note that the appropriate measure from the above would depend on the
underlying distribution highlighted by the variable under question. Mean is considered to be
suitable when the underlying variable has a similar distribution to normal distribution and
hence does not have outliers. However, with skewed variables, a median would be more
relevant since the computation of median is independent on the extreme values and hence

provides a more relevant measure (Hillier, 2016). An example of numerical variable related
measures of central tendency is highlighted below.
From the above, it is apparent that the average age of employees is 41.88 years. Further, 150
of the 300 employees have age not exceeding 42 years. Also, most number of employees in
the company are with an age of 54 years which is the mode. Further, the average years of
experience for the employees stood at 20.71 years. Also, 50 of the 300 employees have years
of experience not exceeding 23 years
With regards to measures of location, the key problem is faced with categorical data since
there are no numerical values. In this case either the median or mode is used which is
essentially based on the identifying the underlying observation belonging to the modal or
median class based on the number of observations (Eriksson & Kovalainen, 2015). An
example of this is indicated below.
In the above case, it is apparent that majority of the employees are from West region of the
country, thus it would be considered the measure of central tendency. Clearly, mean cannot
be computed in such cases.

Further, there is ordinal data which may be represented through the use of numerical values.
This is the case with variables such as job satisfaction where the responses have been
measured on a scale of 1 to 5. Theoretically, it is possible to compute the mean, median and
mode as highlighted below.
It is noteworthy that the above mean value does not provide a faithful and valid summary of
the ordinal data since the same mean value can be arrived at using a plethora of combinations
of responses and hence it is not possible for the user to derive the actual combination that has
been used which limits derivation of meaningful conclusion. As a result, median and mode
are often used in case or ordinal data similar to categorical data (Hillier, 2016).
Descriptive Statistics (Measures of Variation)
Variation represents a key aspect of any data along with location. The various measures of
variation that are commonly used are highlighted as follows (Flick, 2015).
 Range
 Variance
 Standard Deviation
 Inter-Quartile Range (IQR)
 Coefficient of Variation
However, the above variation measures are useful only for numerical data type and do not
apply in case of categorical and normal data type (Eriksson & Kovalainen, 2015).

An example of the application of the above concept in numerical variables is highlighted
below.
Age – With regards to age, it is apparent that the range is 40 which implies that this is
difference between the age of the oldest employee and youngest employee. The coefficient of
variation highlights that the underling variation for age is moderate only. Further, the IQR
implies that the 75 percentile and 25 percentile in terms of age differs by only 18 years.
Years of Experience- With regard to experince, it is apparent that the range is 35 which
implies that this is difference between the most experienced employee and least experienced
employee. The coefficient of variation highlights that the underling variation for experience
is quite high. Further, the IQR implies that the 75 percentile and 25 percentile in terms of
years of experience differs by 15 years.
However, the issue arises in case of both categorical and ordinal variables with regards to
usage of the above measures. Since in categorical variables, there is no numerical data so the
computations are not possible and instead some rough conclusions about variabiltiy can be
drawn from the frequency table (Hair et. al., 2015).
Further, in case of categorical variables, a general observation can be made based on charts or
tables used to represent them. For instance consider the pie chart of city area for the
respondents shown below.

There seems to be moderate variation above since there is not huge difference between the
city area breakup for the employees. However, no precise estimate can be made and further
comparison with other categorical data cannot be enabled (Eriksson & Kovalainen, 2015).
In relation to the ordinal data such as happiness index or job estiamtion, even though the
above measures of variation can be computed but these cannot be used as these are not
reliable and hence have limited information value.
The numerical measures are not relaible for ordinal data since the values are manipulated by
the use of scale. A higher scale to represent the same variable would alter the precise
magnitude (Hastie, Tibshirani & Friedman, 2016).
Data Summary
Frequency for Variables

Graphical Representation

Results and Recommendations
Training & Job Satisfaction

From the above, it is apparent that training has had a significant impact in enhancing the job
satisfaction levels for employees. Thus, the effectiveness of training is established.
Gender Job Satisfaction (Before Training)

The number 2 represents females and these tend to have a lower job satisfaction levels in
comparison with their male counterparts.
Gender Job Satisfaction (After Training)
The job satisfaction level improvement has been better for females as compared to males.
This is confirmed from the fact the before training the males had the higher satisfaction level
which has reversed after training as highlighted above.
Gender & Age

Female representation is dominant with lower age groups i.e. less than 45. However, situation
starts changing after 45 years but the strange observation is post 55 years when males tend to
dominate and this might be indicative of glass ceiling in the company.
Recommendations
The recommendations based on the analysis conducted above include organising training as a
means to enhance job satisfaction at regular intervals. Also, the lower representation of
females in the age group of 55+ needs further analysis to highlight if any glass ceiling exists
and to eliminate the same to enhance job satisfaction.

References
Eriksson, P. and Kovalainen, A. (2015). Quantitative methods in business research (3rd ed.).
London: Sage Publications.
Flick, U. (2015). Introducing research methodology: A beginner's guide to doing a research
project (4th ed.). New York: Sage Publications.
Hair, J. F., Wolfinbarger, M., Money, A. H., Samouel, P., and Page, M. J. (2015). Essentials
of business research methods (2nd ed.). New York: Routledge.
Hastie, T., Tibshirani, R. and Friedman, J. (2016). The Elements of Statistical Learning (4th
ed.). New York: Springer Publications.
Hillier, F. (2016). Introduction to Operations Research. (6th ed.). New York: McGraw Hill
Publications.