MODULE IV
STATISTICS AND PROBABILITY
Lesson 1 Measures of Central Tendency
Lesson 2 Measures of Dispersion
Lesson 3 Normal Distributions
Lesson 4 Odds and Chances
, 2
MODULE IV
Statistics and Probability
INTRODUCTION
Statistics are sets of mathematical equations that are used to analyze
what is happening in the world around us. You've heard that today we live in
the Information Age where we understand a great deal about the world
around us. Much of this information was determined mathematically by
using statistics. When used correctly, statistics tell us any trends in what
happened in the past and can be useful in predicting what may happen in
the future.
In addition, probability and statistics are the mathematics used to
understand chance and to collect, organize, describe, and analyze
numerical data. From weather reports to sophisticated studies of genetics,
from election results to product preference surveys, probability and
statistical language and concepts are increasingly present in the media and
in everyday conversations.
It is also certain that understanding probability and statistics is
essential in the modern world, where the print and electronic media are full
of statistical information and interpretation. The goal of mathematical
instruction in this area should be to make you sensible, critical users of
probability and statistics, able to apply their processes and principles to
real-world problems. You as student should not think that those people who
did not win the lottery yesterday have a greater chance of winning today!
You should not believe an argument merely because various statistics are
offered. Rather, you should be able to judge whether the statistics are
meaningful and are being used appropriately.
Thinking mathematically does not entail knowing the great formulae
and methods of mathematics, but just being logical and applying common
sense. Likewise, if you choose to work instead of setting up your own
business, you can be more productive with great mathematical skills and are
more likely to spell success.
Certainly indispensable, in this lesson, we look at how we can use
statistics and probability as a tool and conceptual foundation in quantitative
reasoning to extract information intelligently and make appropriate
decisions from sea of data for it demarcates our success from failure.
Module IV includes the discussion of the following:
Lesson 1 Measures of Central Tendency
Lesson 2 Measures of Dispersion
Lesson 3 Normal Distributions
Lesson 4 Odds and Chances
Mathematics in the Modern World - Module IV -
, 3
OBJECTIVES
After studying the module you should be able to:
1. Understand the language of statistics.
2. Interpret correctly statistical evidences and form judgments,
conclusions and decisions on the basis of computed data.
3. Transform any normal distribution into the standardized normal
distribution.
4. Use normal distribution table to find probabilities and, inversely,
given z values, to find probabilities.
5. Use and apply the normal distribution in a range of contexts.
6. Define event, outcome, trial, simple event, sample space and
calculate the probability that an event will occur.
7. Calculate the probability of events for more complex outcomes.
8. Solve applications involving probabilities.
9. Appreciate the value of statistical analysis and probability to the
solution of problems having variety of alternative choices.
DIRECTIONS/ MODULE ORGANIZER
1. Module IV consists of four (4) lessons. Take time to read all these four
(4) lessons, so you can have a better understanding and appreciate
about odds and chances, games, and social choices.
2. Accomplish all the learning activities and submit them to your tutor
in the next face-to-face meeting.
3. For difficulties, try to contact the curriculum adviser or your
tutor/professor.
Mathematics in the Modern World - Module IV -
, 4
Lesson 1
MEASURES OF CENTRAL TENDENCY
Statistics is a mathematical science including methods of collecting,
organizing and analyzing data in such a way that meaningful conclusions can
be drawn from them. In general, its investigations and analyses fall into two
broad categories called descriptive and inferential statistics.
Descriptive statistics deals with the processing of data without
attempting to draw any inferences from it. The data are presented in the
form of tables and graphs. The characteristics of the data are described in
simple terms. Events that are dealt with include everyday happenings such
as accidents, prices of goods, business, incomes, epidemics, sports data,
population data.
Inferential statistics is a scientific discipline that uses mathematical
tools to make forecasts and projections by analyzing the given data. This is
of use to people employed in such fields as engineering, economics, biology,
the social sciences, business, agriculture and communications.
Population and Sample
A population often consists of a large group of specifically defined
elements. For example, the population of a specific country means all the
people living within the boundaries of that country.
Usually, it is not possible or practical to measure data for every
element of the population under study. We randomly select a small group of
elements from the population and call it a sample. Inferences about the
population are then made on the basis of several samples.
Qualitative and Quantitative Data
Data is quantitative if the observations or measurements made on a
given variable of a sample or population have numerical values. Example:
height, weight, number of children, blood pressure, current, voltage.
Data is qualitative if words, groups and categories represent the
observations or measurements. Example: colors, yes-no answers, blood
group.
Quantitative data is discrete if the corresponding data value that
can’t take the form of decimals and it is continuous if the data values take
the form of decimals. Example of discrete data: number of children, number
of cars. Example of continuous data: speed, distance, time, pressure.
Mathematics in the Modern World - Module IV -
STATISTICS AND PROBABILITY
Lesson 1 Measures of Central Tendency
Lesson 2 Measures of Dispersion
Lesson 3 Normal Distributions
Lesson 4 Odds and Chances
, 2
MODULE IV
Statistics and Probability
INTRODUCTION
Statistics are sets of mathematical equations that are used to analyze
what is happening in the world around us. You've heard that today we live in
the Information Age where we understand a great deal about the world
around us. Much of this information was determined mathematically by
using statistics. When used correctly, statistics tell us any trends in what
happened in the past and can be useful in predicting what may happen in
the future.
In addition, probability and statistics are the mathematics used to
understand chance and to collect, organize, describe, and analyze
numerical data. From weather reports to sophisticated studies of genetics,
from election results to product preference surveys, probability and
statistical language and concepts are increasingly present in the media and
in everyday conversations.
It is also certain that understanding probability and statistics is
essential in the modern world, where the print and electronic media are full
of statistical information and interpretation. The goal of mathematical
instruction in this area should be to make you sensible, critical users of
probability and statistics, able to apply their processes and principles to
real-world problems. You as student should not think that those people who
did not win the lottery yesterday have a greater chance of winning today!
You should not believe an argument merely because various statistics are
offered. Rather, you should be able to judge whether the statistics are
meaningful and are being used appropriately.
Thinking mathematically does not entail knowing the great formulae
and methods of mathematics, but just being logical and applying common
sense. Likewise, if you choose to work instead of setting up your own
business, you can be more productive with great mathematical skills and are
more likely to spell success.
Certainly indispensable, in this lesson, we look at how we can use
statistics and probability as a tool and conceptual foundation in quantitative
reasoning to extract information intelligently and make appropriate
decisions from sea of data for it demarcates our success from failure.
Module IV includes the discussion of the following:
Lesson 1 Measures of Central Tendency
Lesson 2 Measures of Dispersion
Lesson 3 Normal Distributions
Lesson 4 Odds and Chances
Mathematics in the Modern World - Module IV -
, 3
OBJECTIVES
After studying the module you should be able to:
1. Understand the language of statistics.
2. Interpret correctly statistical evidences and form judgments,
conclusions and decisions on the basis of computed data.
3. Transform any normal distribution into the standardized normal
distribution.
4. Use normal distribution table to find probabilities and, inversely,
given z values, to find probabilities.
5. Use and apply the normal distribution in a range of contexts.
6. Define event, outcome, trial, simple event, sample space and
calculate the probability that an event will occur.
7. Calculate the probability of events for more complex outcomes.
8. Solve applications involving probabilities.
9. Appreciate the value of statistical analysis and probability to the
solution of problems having variety of alternative choices.
DIRECTIONS/ MODULE ORGANIZER
1. Module IV consists of four (4) lessons. Take time to read all these four
(4) lessons, so you can have a better understanding and appreciate
about odds and chances, games, and social choices.
2. Accomplish all the learning activities and submit them to your tutor
in the next face-to-face meeting.
3. For difficulties, try to contact the curriculum adviser or your
tutor/professor.
Mathematics in the Modern World - Module IV -
, 4
Lesson 1
MEASURES OF CENTRAL TENDENCY
Statistics is a mathematical science including methods of collecting,
organizing and analyzing data in such a way that meaningful conclusions can
be drawn from them. In general, its investigations and analyses fall into two
broad categories called descriptive and inferential statistics.
Descriptive statistics deals with the processing of data without
attempting to draw any inferences from it. The data are presented in the
form of tables and graphs. The characteristics of the data are described in
simple terms. Events that are dealt with include everyday happenings such
as accidents, prices of goods, business, incomes, epidemics, sports data,
population data.
Inferential statistics is a scientific discipline that uses mathematical
tools to make forecasts and projections by analyzing the given data. This is
of use to people employed in such fields as engineering, economics, biology,
the social sciences, business, agriculture and communications.
Population and Sample
A population often consists of a large group of specifically defined
elements. For example, the population of a specific country means all the
people living within the boundaries of that country.
Usually, it is not possible or practical to measure data for every
element of the population under study. We randomly select a small group of
elements from the population and call it a sample. Inferences about the
population are then made on the basis of several samples.
Qualitative and Quantitative Data
Data is quantitative if the observations or measurements made on a
given variable of a sample or population have numerical values. Example:
height, weight, number of children, blood pressure, current, voltage.
Data is qualitative if words, groups and categories represent the
observations or measurements. Example: colors, yes-no answers, blood
group.
Quantitative data is discrete if the corresponding data value that
can’t take the form of decimals and it is continuous if the data values take
the form of decimals. Example of discrete data: number of children, number
of cars. Example of continuous data: speed, distance, time, pressure.
Mathematics in the Modern World - Module IV -
