1. What is Statistics? Discuss its importance.
Answer:
Statistics is the science concerned with developing and studying
methods for collecting, analyzing, interpreting, and presenting empirical data. It is
an interdisciplinary field. It is used in almost all scientific fields. In fact, statistics
plays a vital role in every field of human activity. It helps in determining the existing
position of per capita income, unemployment, population growth rates, housing,
and schooling medical facilities in a country.
2. What are the areas of Statistics?
Answer:
Statistics are generally divided into two broad categories which are
Descriptive Statistics and Inferential Statistics. Descriptive statistics involves
data collection, processing, classification, and reporting. Inferential statistics
focuses on drawing general conclusions from a sample regarding a population
characteristic. In other words, descriptive statistics describe the properties of
sample and population data, while inferential statistics use those properties to
test hypotheses and draw conclusions.
3. Compare Sample and Population. Discuss extensively.
Answer:
A population includes all members from a specified group, all possible
outcomes or measurements that are of interest. The exact population will
depend on the scope of the study. For example, say you would like to know
whether there is an association between job performance and the amount of
home working hours per week in the specific case of Belgian data scientists. In
this case, the population might be Belgian data scientists. However, if the scope
of the study is more narrow (e.g., the study focuses on french-speaking Belgian
data scientists who live at least 30km away from their workplace), then the
population will be more specific and include only workers who meet the criteria.
The point is that the population should only include people to whom the results
will apply.
A sample consists of some observations drawn from the population,
so a part or a subset of the population. The sample is the group of elements who
actually participated in the study. For instance, the population may be “all people
living in Belgium” and the sample may be “some people living in Belgium”. It can
be anything else too. Say you are testing the effect of a new fertilizer on crop
yield. All the crop fields represent your population, whereas the 10 crop fields
you tested correspond to your sample. Since a sample is a subset of a
population, a sample is always smaller than the population. Note that a
population must not necessarily be large. To summarize, the sample is the group
of individuals who participated in the study and the population is the broader
group to whom the results will apply. Measurements of the entire population are
often too complex or impossible, so representative samples are used to draw
conclusions about the population. Samples based on a random selection are
often the most representative samples. In simpler words, a population is an
entire group that you want to draw conclusions about. A sample is a specific
group that you will collect data. The size of the sample is always less than the
total size of the population.
4. Define and provide examples of the following:
Variable
It is defined as any characteristics, number, or quantity that can be
measured or counted. It may also be called a data item. Examples of this are
age, sex, business income and expenses, country of birth, capital expenditure,
class grades, eye color, and vehicle type.
Data
Data are individual pieces of factual information recorded and used for
the purpose of analysis. It is the raw information from which statistics are
created. Statistics are the results of data analysis. Examples of this are finncial
and economics data, census, price of a product, transactional data and others.
Data is the plural of datum. It is a piece of information. The data can be
classified into two general categories: quantitative data and qualitative data.
The quantitative data can further be classified as numerical data that can be
either discrete or continuous. The qualitative data can be further sub-divided
into nominal, ordinal, and binary data. Qualitative data represent that
information that can be classified by some quality, characteristics or criterion.
For example, the colour of a car, religion, blood type, and marital status.
Experiment
It is the procedure of drawing a sample with the intention of making
a decision. The sample values are to be regarded as the values of a random
variable defined on some measurable space, and the decisions made are to be
functions of this random variable.
Parameter
Is any measured quantity of a statistical population that summarises
or describes an aspect of the population, such as a mean or a standard
deviation. In addition, a parameter is a number describing a whole population
(e.g., population mean), while a statistic is a number describing a sample (e.g.,
sample mean). The goal of quantitative research is to understand
characteristics of populations by finding parameters.
Statistic
Also called as a smple statistic is any quantity computed from values
in a sample which is considered for a statistical purpose. Statistical purposes
include estimating a population parameter, describing a sample, or evaluating
a hypothesis. The average (or mean) of sample values is a statistic.
5. What are the two kinds of Variables? Discuss extensively.
Answer:
The two kinds of variables are the Qualitative variable and the Quantitative
variable. Qualitative variable is also called a categorical variable which shows the
quality or properties of the data. It is represented by a name, a symbol, or a
number code. These scales are mutually exclusive (no overlap) and none of them
have any numerical significance. It has two types qhich are the nominal and the
ordinal. On the other hand, a Quantitative variable is the data that show some
quantity through numerical value. Quantitative data are the numeric variables
(e.g., how many, how much, or how often). Age, blood pressure, body
temperature, hemoglobin level, and serum creatinine level are some examples of
quantitative data. It is also called metric data. Discrete and Continuous. variables
are quantitative variables.
6. Define and discuss extensively the levels of data the:
Nominal Variable - is a qualitative data that are simply names or properties
having two or more categories, and there is no intrinsic ordering to the
categories, i.e., data have no natural ranking or ordering. For example, gender
(male and female) and marital status (married/unmarried) have two categories,
but these categories have no natural order or ranking
Ordinal Variable - It is also a qualitative data that is similar to a nominal variable.
The difference between the two is that there is a clear ordering in the data, i.e.,
ordinal data, unlike nominal data, have some order. For example, ordinal scales
are seen in questions that call for ratings of quality (very good, good, fair, poor,
very poor), agreement (strongly agree, agree, disagree, strongly disagree),
economic status (low, medium, and high), etc. All the ranking data including
Likert scales, Bristol stool scale, and all the other scales which are ranked
between 0 and 10 are also called ordinal data.
Discrete Variable - It is quantitative data, but its values cannot be expressed or
presented in the form of a decimal; for example, number of males, number of
females, number of patients, and family size cannot expressed in decimal in a
meaningful way.
Continuous Variable - this belongs to quantitative data. Data are measured in
values and can be quantified and presented in decimals. Age, height, weight,
body mass index, serum creatinine, heart rate, systolic blood pressure, and
diastolic blood pressure are some examples.
7. What are the importance of measurement?
Answer:
Measurement in the first place is the process of systematically assigning
numbers to objects and their properties to facilitate the use of mathematics in
studying and describing objects and their relationships. Some types of
measurement are fairly concrete: for instance, measuring a person’s weight in
pounds or kilograms or his height in feet and inches or in meters. Measurement
scale is an important part of data collection, analysis, and presentation. The
importance of measurement is important to be able to determine the type of
statistical analysis that can be conducted, and, therefore, the type of conclusions
that can be drawn from the research.