This document contains a lesson on probability distributions and calculating the mean, variance, and standard deviation. It includes examples of probability distributions and step-by-step instructions for calculating the key statistics. Students are asked questions to practice these calculations and assess their understanding of mean, variance, and standard deviation in the context of probability distributions.

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MODULE 1 –
LESSON 3
Republic of the Philippines
Department of Education
Region XII
Division of Sultan Kudarat
KALAMANSIG NATIONAL HIGH SCHOOL
Kalamansig, Sultan Kudarat

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PAGBABALIK SA NAKARAAN
State the process of
determining possible outcomes
of the random experiment.
How to determine its
probabilities?

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ACTIVITY 1: YOU WANT TO BE ENGAGED?
Question 1 Answer
1,680

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ACTIVITY 1: YOU WANT TO BE ENGAGED?
Question 2
In how many ways can you
arrange the letters of the word
PROBABILITY?

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ACTIVITY 1: YOU WANT TO BE ENGAGED?
Question 2 Answer
9,979, 200

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ACTIVITY 1: YOU WANT TO BE ENGAGED?
Question 3
How many ways can you sit 10
people in a round table with to
sits?

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ACTIVITY 1: YOU WANT TO BE ENGAGED?
Question 3 Answer:
362, 880

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ACTIVITY 1: YOU WANT TO BE ENGAGED?
Arrange and supply the missing
vowel of the following:

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ACTIVITY 1: YOU WANT TO BE ENGAGED?
Question 4:
it is also known as the expected
value, the weighted average of
the possible values.
NM _____ _____

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ACTIVITY 1: YOU WANT TO BE ENGAGED?
Question 4: ANSWER
MEAN

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ACTIVITY 1: YOU WANT TO BE ENGAGED?
Question 5: It is also known as
the measure of spread and
dispersion, it measures the
variation of the values from the
mean.

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ACTIVITY 1: YOU WANT TO BE ENGAGED?
NCVR ____ _____ ____ _____

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ACTIVITY 1: YOU WANT TO BE ENGAGED?
Question 5 ANSWER
VARIANCE

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LEARNING OBJECTIVES
At the end of the lesson; the
students should be able to:
1. Solve the mean variance and
standard deviation of the
probability distribution

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ACTIVITY 2: EXPLORE THE WORLD
Question:
1. In your own understanding what is Mean?
2.) What is variance and standard deviation?
3.) Is true that when mean is computed,
standard deviation is not already necessary?

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ACTIVITY 2: EXPLORE THE WORLD
1. In a 5-item test, the probabilities that
a student gets 0, 1, 2, 3, 4, or 5
mistakes are 3/20, 5/20, 7/20, 3/20,
1/20, and 120, respectively. What is the
average number of mistakes that a
student makes in this class? What is
the variance and standard deviation of
this discrete probability distribution?

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ACTIVITY 2: EXPLORE THE WORLD
Follow the process and procedures in computing the
Mean, variance and Standard deviation of the
probability distribution
1. The column 1, denoted by X is the values of the
random variables. The column denoted by P(X) is the
probability of the random variables. Step 1: Multiply
the values of the random variables of the random
variable (X) to its probability to give the result of the
third column X . P(X) respectively.
2. To find the mean or average of the distribution find
the total or summation of X . P(X) in the third
column given by the formula: 𝜇 = σ 𝑋 . 𝑃(𝑋)

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ACTIVITY 2: EXPLORE THE WORLD
3. Subtract the mean (𝜇) to the values of the
random variable (x) in the first column, the
result is at fourth column denoted by x - 𝜇.
4. Square the result in the fourth column,
the results are listed on the fifth column
(𝑥 − 𝜇)2.
5. Multiply the fifth column (𝑥 − 𝜇)2
to the
second column P(X)

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ACTIVITY 2: EXPLORE THE WORLD
3. Subtract the mean (𝜇) to the values of the
random variable (x) in the first column, the
result is at fourth column denoted by x - 𝜇.
4. Square the result in the fourth column,
the results are listed on the fifth column
(𝑥 − 𝜇)2.
5. Multiply the fifth column (𝑥 − 𝜇)2
to the
second column P(X)

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ACTIVITY 2: EXPLORE THE WORLD
6. Compute for variance using the formula:

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ACTIVITY 3: LET ME EXPLAIN
WHAT IS MEAN?
- expected value, is obtained by integrating the product
of the variable with its probability as defined by the
distribution.
WHAT IS VARIANCE?
The expectation of the squared deviation of a
random variable from its population mean or sample
mean. Variance is a measure of dispersion, meaning it is
a measure of how far a set of numbers is spread out
from their average value.

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ACTIVITY 3: LET ME EXPLAIN
Lets go back to the problem:
1. In a 5-item test, the probabilities that
a student gets 0, 1, 2, 3, 4, or 5
mistakes are 3/20, 5/20, 7/20, 3/20,
1/20, and 120, respectively. What is the
average number of mistakes that a
student makes in this class? What is the
variance and standard deviation of this
discrete probability distribution?

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ACTIVITY 3: LET ME EXPLAIN

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ACTIVITY 3: LET ME EXPLAIN
Compute for the standard deviation.
Simply find the square root of the
variance we have: 1.28 respectively.

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ACTIVITY 3: LET ME EXPLAIN
2. In a seafood restaurant, the manager
wants to know if their customers like their
new raw large oysters. According to their
sales representative, in the past 4 months,
the number of oysters consumed by a
customer, along with its corresponding
probabilities, is shown in the succeeding
table. Compute the mean, variance and
standard deviation.

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ACTIVITY 3: LET ME EXPLAIN

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ACTIVITY 3: LET ME EXPLAIN

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ACTIVITY 3: LET ME EXPLAIN

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ACTIVITY 3: LET ME EXPLAIN
3. The probabilities that 4, 5, 6, 7, 8, 9, or
10 accidents happen in Northern Mindanao
High Way in a year is 0.45, 0.22, 0.15,
0.10, 0.05, 0.02, and 0.01, respectively.
Find the average number of accidents that
occur in the said high way each year.

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ACTIVITY 3: LET ME EXPLAIN

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ACTIVITY 3: LET ME EXPLAIN

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ACTIVITY 4 - ELABORATE
Practice: Answer the following problems
1. Students were asked to estimate the
length of the table in inches. The errors in
the estimated values were recorded x (3, 4,
5, 6, 7) and p(x) = 0.025, 0.1, 0.3, 0.15, 0.2
respectively. Compute for mean, variance
and standard deviation of the probability
distribution.

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ACTIVITY 4 - ELABORATE
Practice: Answer the following problems
2. The report of a weather bureau on the
forecast of the number of typhoons entering
the country’s area of responsibility. x = 0, 1,
2, 3, 4. p(x) = 0.15, 0.35, 0.30, 0.10, 0.10.
find the mean, variance and standard
deviation.

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ACTIVITY 4 - ELABORATE
Practice: Answer the following problems
3. A certain company recently opened some
job opportunities. x = 1, 2, 3, 4, 5 and p(x) =
0.1, 0.15, 0.16, 0. 29 and 0.3 respectively.
find the mean, variance and standard
deviation.

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ACTIVITY 5 - Quiz
Answer the following problems
1. Suppose that the number of cars, that
pass through a car care center between
1:00 pm and 3:00 pm on a Sunday. Let x =
3, 4, 5, 6, 7, 8 and p(x) = 1/3 , ¼, 1/3, ¼, ¼,
1/6. find the mean variance and standard
deviation

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ACTIVITY 5 - Quiz
Answer the following problems
2. The number of cars sold per day at a
local car dealership, along with its
corresponding probabilities. x = 0, 1, 2, 3, 4
and p(x) = 1/10, 2/10, 3/10, 2/10 and 2/1o.
solve for mean, variance and standard
deviation of the probability distribution.

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ACTIVITY 5 - Quiz
Answer the following problems
3. When 3 coins are tossed, the probability
distribution for the random variables X
representing the number of the heads that
occur: x = 0, 1, 2, 3. p(x) = 1/8, 3/8, 6/8, 3/8.
Solve for mean, variance and standard
deviation.