This presentation serves as an instructional material for Statistics and Probability subject in Grade 11.

1. STATISTICS AND
PROBABILITY
ALEMAR B. MAPINOGOS

2. • Statistics is the science of conducting studies to
collect, organize, summarize, analyze, and draw
conclusions from data.
✓Historical Note: A Scottish landowner and president of
the Board of Agriculture, Sir John Sinclair introduced
the word statistics into the English language in the
1798 publication of his book on a statistical account of
Scotland. The word statistics is derived from the Latin
word status, which is loosely defined as a statesman.

3. • A variable is a characteristic or attribute that can
assume different values.
• Data are the values (measurements or observations) that
the variables can assume.
• Variables whose values are determined by chance are
called random variables.
• A collection of data values forms a data set. Each value
in the data set is called a data value or a datum.

4. • 2 Areas/Fields of Statistics
1. Descriptive statistics
2. Inferential statistics
• Descriptive statistics consists of the collection, organization,
summarization, and presentation of data.
✓In descriptive statistics the statistician tries to describe a situation.
Consider the national census conducted by the U.S. government
every 10 years. Results of this census give you the average age,
income, and other characteristics of the U.S. population. To obtain
this information, the Census Bureau must have some means to
collect relevant data. Once data are collected, the bureau must
organize and summarize them. Finally, the bureau needs a means
of presenting the data in some meaningful form, such as charts,
graphs, or tables.

5. • Inferential statistics consists of generalizing from samples to
populations, performing estimations and hypothesis tests,
determining relationships among variables, and making
predictions.
✓making inferences from samples to populations
✓uses probability
✓hypothesis testing
✓relationships among variables
✓Making predictions

6. • Inferential statistics
✓ Here, the statistician tries to make inferences from samples to
populations. Inferential statistics uses probability, i.e., the chance
of an event occurring. You may be familiar with the concepts of
probability through various forms of gambling. If you play cards,
dice, bingo, or lotteries, you win or lose according to the laws of
probability.

7. TRY THIS OUT!
Determine whether descriptive or inferential statistics were
used.
a. The average jackpot for the top five lottery winners was $367.6
million.
b. A study done by the American Academy of Neurology suggests
that older people who had a high caloric diet more than doubled
their risk of memory loss.
c. Based on a survey of 9317 consumers done by the National
Retail Federation, the average amount that consumers spent on
Valentine’s Day in 2011 was $116.
d. Scientists at the University of Oxford in England found that a
good laugh significantly raises a person’s pain level tolerance.

8. • A population consists of all subjects (human or
otherwise) that are being studied.
• A sample is a group of subjects selected from a
population.
• An area of inferential statistics called hypothesis testing
is a decision-making process for evaluating claims about
a population, based on information obtained from
samples.

9. Variables and Types of Data
• Qualitative variables
• Quantitative variables

10. Variables and Types of Data
• Qualitative variables are variables that can be placed into
distinct categories, according to some characteristic or
attribute.
✓For example, if subjects are classified according to
gender (male or female), then the variable gender is
qualitative. Other examples of qualitative variables are
religious preference and geographic locations.

11. Variables and Types of Data
• Quantitative variables are numerical and can be ordered
or ranked.
✓For example, the variable age is numerical, and people
can be ranked in order according to the value of their
ages. Other examples of quantitative variables are heights,
weights, and body temperatures.

12. Quantitative variables can be further classified into two
groups:
• Discrete variables
• Continuous variables

13. • Discrete variables assume values that can be counted.
Example:
1. number of children in a family
2. number of students in a classroom
3. number of calls received by a switchboard operator
each day for a month.

14. • Continuous variables can assume an infinite number of
values between any two specific values. They are
obtained by measuring. They often include fractions and
decimals.
✓Temperature, for example, is a continuous variable,
since the variable can assume an infinite number of
values between any two given temperatures.

15. TRY THIS OUT!
Classify each variable as a discrete variable or a
continuous variable.
a. The highest wind speed of a hurricane
b. The weight of baggage on an airplane
c. The number of pages in a statistics book
d. The amount of money a person spends per year for
online purchases

17. • Continuous variables can assume an infinite number of
values between any two specific values. They are
obtained by measuring. They often include fractions and
decimals.
✓Temperature, for example, is a continuous variable,
since the variable can assume an infinite number of
values between any two given temperatures.

18. • Probability- is the likelihood of occurrence of an event.
• Experiment- is an activity that is under consideration and which can
be done repeatedly.
Examples:
1. Drawing a card from an ordinary deck of 52 cards.
2. Tossing a coin
3. Rolling a die
• Sample Space- is the set of all possible outcomes of an experiment.
Examples:
1. In tossing a coin, the possible outcomes are head or tail. Hence
the sample space is 𝑺 = {𝑯, 𝑻}.
2. In rolling a die, the sample space is 𝑺 = {𝟏, 𝟐, 𝟑, 𝟒, 𝟓, 𝟔}.

19. • Sample point- is the element of the sample space. Thus, in
tossing a coin, there are two sample points: head and tail.
• Event- is any subset of the sample space. A simple event is one
that consists of exactly one outcome, hence it cannot be
decomposed. On the other hand, an even is compound it consists
of more than one outcome.
• The complement of an event A with respect to the sample space S
is the set of all elements of S that are not in A (denoted by A^').
• Random Variable- is a variable whose possible values are
determined by chance.

20. RANDOM VARIABLE
• It is typically represented by an uppercase letter, usually
𝑿, while its corresponding lowercase letter in this case, x,
is used to represent one of its values.
Example: A coin is tossed thrice. Let the variable X
represent the number of heads that results from this
experiment.

21. • Example: A coin is tossed thrice. Let the variable X
represent the number of heads that results from this
experiment.

22. • In the illustration, random variable is represented by
the upper case 𝑿. The lower case 𝒙 represents the
specific values. Hence, 𝒙 = 𝟑,𝒙 = 𝟐, 𝒙 = 𝟏, 𝒙 = 𝟐, 𝒙 =
𝟏, 𝒙 = 𝟏,and 𝒙 = 𝟎.
• The sample space for the possible outcomes is
𝑺 = 𝑯𝑯𝑯, 𝑯𝑯𝑻, 𝑯𝑻𝑯, 𝑯𝑻𝑻, 𝑻𝑯𝑯, 𝑻𝑯𝑻, 𝑻𝑻𝑯, 𝑻𝑻𝑻 .
The value of the variable 𝑿 can be 𝟎, 𝟏, 𝟐, 𝒐𝒓 𝟑. Then in
this example, 𝑿 is a random variable.

23. • Random variables can either be DISCRETE or
CONTINUOUS
A discrete random variable can only take a
finite (countable) number of distinct values.
Distinct values mean values that are exact and
can be represented by nonnegative whole
numbers.

24. • Examples:
• 𝑳𝒆𝒕 𝑿 = number of students randomly selected to be
interviewed by a researcher. This is a discrete random
variable because its possible values are 0, 1, or 2, and so
on.
• 𝑳𝒆𝒕 𝒀 = number of left-handed teachers randomly
selected in a faculty room. This is a discrete random
variable because its possible values are 0, 1, or 2, and so
on.
• 𝑳𝒆𝒕 𝒁 =number of defective light bulbs among randomly
selected light bulbs. This is a discrete random variable
because the number of defective light bulbs, which X can
assume, are 0, 1, 2, and so on.

25. A continuous random variable can assume an infinite
number of values in an interval between two specific
values. This means they can assume values that can be
represented not only by nonnegative whole numbers but
also by fractions and decimals. These values are often
results of measurements.

26. Examples:
• 𝐿𝑒𝑡 𝑋 = the lengths of randomly selected shoes of senior
students in centimeters. The lengths of shoes of the
students can be between any two given lengths. The
values can be obtained by using a measuring device, a
ruler. Hence, the random variable 𝑋 is a continuous
random variable.
• 𝐿𝑒𝑡 𝑍 = the hourly temperatures last Sunday.
• 𝐿𝑒𝑡 𝑌 = the heights of daisy plants in the backyard.