What Is Statistics?
Descriptive statistics deals with methods of organizing, summarizing, and presenting data in
a convenient and informative way. One form of descriptive statistics uses graphical
techniques that allow statistics practitioners to present data in ways that make it easy for the
reader to extract useful information. Another form uses numerical techniques to summarize
data, for example calculating average or mean.
Inferential statistics is a body of methods used to draw conclusions or inferences about
characteristics of populations based on sample data.
Statistical inference problems involve three key concepts: the population, the sample and
the statistical inference. A population is the group of all items of interest to a statistics
practitioner. It does not necessarily refer to a group of people, it can, for example, refer to the
population of ball bearings produces at a large plant. The descriptive measure of a population
is called a parameter. In most applications of inferential statistics, the parameter represents
the information we need. A sample is a set of data drawn from the studied population and the
descriptive measure of a sample is called a statistic. We use statistics to make inferences
about parameters. A statistical inference is the process of making an estimate, prediction, or
decision about a population based on sample data. Populations are almost always very large,
investigating each member of the population would be expensive and impractical. Therefore,
it is far easier and cheaper to take a sample from the population of interests and draw
conclusions or make estimates about the population about the population on the basis of
information provided by the sample. The conclusion drawn from such conclusion and
estimates are not always going to be correct. To measure how correct is it, we have two
measures called: the confidence level and the significance level. The confidence level is the
proportion of times that an estimating procedure will be correct. The significance level
measures how frequently the conclusion will be wrong.
Excel can perform statistical procedures in many different ways including: Statistical,
spreadsheets, analysis toolpak and XLSTAT.
Graphical Descriptive Techniques I
The objective of statistics is to extract information from data, and there are different types of
data and information. To help explain this principle, we have some terms that needs to be
defined. A variable is some characteristic of a population or sample, for example the mark on
a statistics exam. The mark will vary from student to student, thus the name variable. The
values of the variable are the possible observations of the variable. For example, the values of
statistics exam marks are integers between 0 and 100 (assuming the exam is marked out of a
100). Data are the observed values of a variable; data is plural for datum. There are three
types of data: interval, nominal, and ordinal.
Interval data are real numbers, such as heights, weights, incomes, and distances. We also
refer to this type as quantitative or numerical. All calculations are valid, it is the most
restricting data type and a continuous data type. This data type can also be treated as ordinal
or nominal.
1
, Nominal data are values that are arbitrary numbers that represent categories. For example,
responses to questions about marital status produce nominal data or country codes. They are
also called quantitative or categorical. Only calculations based on the frequencies or
percentages of occurrences are valid and the data cannot be treated as ordinal or nominal.
You cannot add or subtract the data, and you cannot compare results. Nominal data is at the
bottom of the hierarchy of data, because no calculations other than determination frequencies
are permitted.
Ordinal data are values that must represent the ranked order of the data. For example,
temperature. Calculations are based on an ordering process are valid. This data type can be
treated as nominal but not interval.
There are no specific graphical techniques for ordinal data. When we wish to describe a set of ordinal
data, we treat the data as if they were nominal and use the techniques in this section. The only
criterion is that the bars in bar charts should be arranged in ascending (or descending) ordinal values.
In pie charts, the wedges are normally arranged clockwise in ascending or descending order.
Factors that identify when to use frequency and relative frequency tables, and bar and pie charts:
1) Objective: describe a single set of data.
2) Data type: nominal and ordinal
Univariate are techniques applied to single sets of data, and there are many situations where we wish
to depict the relationship between variables; in such cases, Bivariate methods are required. A cross-
classification table (crosstabulation table) is used to describe the relationship between two nominal
variables. A variation of the bar chart is employed to graphically describe the relationship. The same
technique is used to compare two or more sets of nominal data. To describe the relationship between
two nominal variables, we must remember that we are permitted only to determine the frequency of
the values. If we have two or more sets of nominal data we need to see if the differences exist
between the columns of the frequency distributions (or between the bar charts), then we can conclude
that differences exist among the three populations.
There are several ways to store the data to be used to produce a table, a bar chart, or a pie chart. First,
the data are in two columns, the first column represent the categories of the first nominal variable and
the second column store the categories for the second. Each row represents one observation of the two
variables, and the number of observations in each column must be the same. Second, the data are store
in two or more columns, with each column representing the same variable in a different sample or
population. Lastly, the table representing the counts in a cross-classification table may have already
been created.
Factors that identify when to use a cross-classification table:
1) Objective: describe the relationship between two variables and compare two or more sets of
data.
2) Data type: nominal.
Graphical Descriptive Techniques II
Histogram: graphical technique used to summarize a set of interval data. It is created by drawing
rectangles whose bases are the intervals and whose heights are the frequencies.
2
Descriptive statistics deals with methods of organizing, summarizing, and presenting data in
a convenient and informative way. One form of descriptive statistics uses graphical
techniques that allow statistics practitioners to present data in ways that make it easy for the
reader to extract useful information. Another form uses numerical techniques to summarize
data, for example calculating average or mean.
Inferential statistics is a body of methods used to draw conclusions or inferences about
characteristics of populations based on sample data.
Statistical inference problems involve three key concepts: the population, the sample and
the statistical inference. A population is the group of all items of interest to a statistics
practitioner. It does not necessarily refer to a group of people, it can, for example, refer to the
population of ball bearings produces at a large plant. The descriptive measure of a population
is called a parameter. In most applications of inferential statistics, the parameter represents
the information we need. A sample is a set of data drawn from the studied population and the
descriptive measure of a sample is called a statistic. We use statistics to make inferences
about parameters. A statistical inference is the process of making an estimate, prediction, or
decision about a population based on sample data. Populations are almost always very large,
investigating each member of the population would be expensive and impractical. Therefore,
it is far easier and cheaper to take a sample from the population of interests and draw
conclusions or make estimates about the population about the population on the basis of
information provided by the sample. The conclusion drawn from such conclusion and
estimates are not always going to be correct. To measure how correct is it, we have two
measures called: the confidence level and the significance level. The confidence level is the
proportion of times that an estimating procedure will be correct. The significance level
measures how frequently the conclusion will be wrong.
Excel can perform statistical procedures in many different ways including: Statistical,
spreadsheets, analysis toolpak and XLSTAT.
Graphical Descriptive Techniques I
The objective of statistics is to extract information from data, and there are different types of
data and information. To help explain this principle, we have some terms that needs to be
defined. A variable is some characteristic of a population or sample, for example the mark on
a statistics exam. The mark will vary from student to student, thus the name variable. The
values of the variable are the possible observations of the variable. For example, the values of
statistics exam marks are integers between 0 and 100 (assuming the exam is marked out of a
100). Data are the observed values of a variable; data is plural for datum. There are three
types of data: interval, nominal, and ordinal.
Interval data are real numbers, such as heights, weights, incomes, and distances. We also
refer to this type as quantitative or numerical. All calculations are valid, it is the most
restricting data type and a continuous data type. This data type can also be treated as ordinal
or nominal.
1
, Nominal data are values that are arbitrary numbers that represent categories. For example,
responses to questions about marital status produce nominal data or country codes. They are
also called quantitative or categorical. Only calculations based on the frequencies or
percentages of occurrences are valid and the data cannot be treated as ordinal or nominal.
You cannot add or subtract the data, and you cannot compare results. Nominal data is at the
bottom of the hierarchy of data, because no calculations other than determination frequencies
are permitted.
Ordinal data are values that must represent the ranked order of the data. For example,
temperature. Calculations are based on an ordering process are valid. This data type can be
treated as nominal but not interval.
There are no specific graphical techniques for ordinal data. When we wish to describe a set of ordinal
data, we treat the data as if they were nominal and use the techniques in this section. The only
criterion is that the bars in bar charts should be arranged in ascending (or descending) ordinal values.
In pie charts, the wedges are normally arranged clockwise in ascending or descending order.
Factors that identify when to use frequency and relative frequency tables, and bar and pie charts:
1) Objective: describe a single set of data.
2) Data type: nominal and ordinal
Univariate are techniques applied to single sets of data, and there are many situations where we wish
to depict the relationship between variables; in such cases, Bivariate methods are required. A cross-
classification table (crosstabulation table) is used to describe the relationship between two nominal
variables. A variation of the bar chart is employed to graphically describe the relationship. The same
technique is used to compare two or more sets of nominal data. To describe the relationship between
two nominal variables, we must remember that we are permitted only to determine the frequency of
the values. If we have two or more sets of nominal data we need to see if the differences exist
between the columns of the frequency distributions (or between the bar charts), then we can conclude
that differences exist among the three populations.
There are several ways to store the data to be used to produce a table, a bar chart, or a pie chart. First,
the data are in two columns, the first column represent the categories of the first nominal variable and
the second column store the categories for the second. Each row represents one observation of the two
variables, and the number of observations in each column must be the same. Second, the data are store
in two or more columns, with each column representing the same variable in a different sample or
population. Lastly, the table representing the counts in a cross-classification table may have already
been created.
Factors that identify when to use a cross-classification table:
1) Objective: describe the relationship between two variables and compare two or more sets of
data.
2) Data type: nominal.
Graphical Descriptive Techniques II
Histogram: graphical technique used to summarize a set of interval data. It is created by drawing
rectangles whose bases are the intervals and whose heights are the frequencies.
2
