Business Statistics: Descriptive and Inferential Statistics

Business Statistics
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QUESTION 1
1. Statistics: An aggregate of facts which are affected by a number of causes and which are
expressed numerically to some reasonable extent of accuracy and which are collected in a
systematic manner for a specific purpose is called statistics (MANN, 2017).
Similar to almost every field of study, applied statistics can be categorised into two types of
statistics, which are descriptive and inferential statistics.
Descriptive statistics: Methods for displaying, organizing, and describing data by graphs,
tables, and summary measures are called descriptive statistics. Mean, median, mode are
some examples of descriptive statistics.
Typically, the recording of data is usually in much unorganized form. Therefore, this data
set is not very useful for conclusions or decisions. It is easier to draw conclusions from the
database summary. Therefore, by creating tables, charts, or estimates of aggregates (as a
Median, Mean) one can reduce the amount of data to a manageable size. Descriptive
statistics are provided by statistical information that helps to perform this statistical
analysis.
Inferential Statistics: The method for predicting or determining a population based on
test results is called inferential statistics (ANDERSON, 2019). T-test, F-test, Chi-square test
are few examples of inferential statistics.
Most statistics are based on the results of the sample and forecasts, predictions and
decisions about population are made. Statistics involving such decision procedures are
called inferential statistics or inductive statistics.
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2. Two main kinds of data are quantitative or numerical, and qualitative or subjective data.
Summary of types of data
Quantitative Data: for countable measurements of observation comes numerical or
quantitative data. This type of data can be classified into two categories, discrete and
continuous (Silverman, 2016).
Discrete Data: A quantitative measurement is called discrete if the measurements are
countable / integers in nature. For example, number of cigarettes smoked in a day,
number of students in a class, or number of members in a household are all discrete data.
Continuous Data: A quantitative measurement when taken on any value within a particular
range (including all real values) is called a continuous data (Treiman, 2014).
For example, height and weight of person are continuous measurements or continuous
data.
Qualitative Data: This type of data generates from observations separated into distinct
classifications. Two types of qualitative data are nominal and ordinal data.
Nominal Data: A qualitative measurement without any order among the categories is
known as nominal data.
For example, sex and eye colour are some examples of nominal data.
Ordinal Data: A qualitative data with some kind of ordering is known as ordinal data. This
sense of ordering may not be numerical in nature (Treiman, 2014).
For example, socio economic status, age group are some examples of ordinal data.
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QUESTION 2
a The frequency distribution for the quarterly sales revenues (‘000) of Gymnasium
equipment has been constructed as below. The class midpoints have been evaluated by
considering the average of the class limits. The class boundaries have been evaluated
from the class limits for continuous representation of the data. The class limits have been
adjusted by 0.5 (Lower class limit of the class – upper class limit of the previous class) on
both ends of a class (subtracted from left hand class limit and added to the right hand
class limit) to find the class boundaries (Bluman, 2009).
For the first class, lower class boundary has been evaluated as = 26 – (0.5) = 25.5 and the
upper class boundary has been evaluated as = 35 + (36 – 35)/2 = 35 + 0.5 = 35.5.
Similarly, all the class boundaries have been calculated. Tally marks have been used to
count the number of observations from the quarterly sales data table which falls within the
class limits. The final frequency table has been presented in Table 2.
Table 1: Frequency and Class Boundary Calculations
Class interval
(‘000)
Class
Boundaries
Tally Mark
26-35 25.5-35.5 IIII IIII I
36-45 35.5-45.5 IIII IIII
46-55 45.5-55.5 IIII
56-65 55.5-65.5 IIII
66-75 65.5-75.5 IIII
76-85 75.5-85.5 I
86-95 85.5-95.5 I
96-105 95.5-105.5
106-115 105.5-115.5 I
Table 2: Frequency Distribution Table with Class Boundaries
Class interval Class Class Midpoint Frequency
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