a lesson ppt for normal distribution

1. Jonnah Mariz Nacar - Bernal
Math Teacher
|| jmgnacar@gmail.com ||
Probability and Statistics
PROBABILITY
and
STATISTICS

2. Jonnah Mariz Nacar - Bernal
Math Teacher
|| jmgnacar@gmail.com ||
Probability and Statistics
Computing VARIANCE of
a discrete probability
distribution

3. Jonnah Mariz Nacar - Bernal
Math Teacher
|| jmgnacar@gmail.com ||
Probability and Statistics
Objectives of the lesson
At the end of the lesson, you can:
a. Illustrate and calculate the variance of a
discrete random variable
b. Interpret the variance of a discrete
random variable; and
c. Solve problems involving variance of
probability distribution.

4. Jonnah Mariz Nacar - Bernal
Math Teacher
|| jmgnacar@gmail.com ||
Probability and Statistics
Variance and
standard deviation
• The term variance refers to a statistical measurement of the spread
between numbers in a data set.
• Variance measures how far each number in the set is from
the mean (average), and thus from every other number in the set.
• The variance and standard deviation describe the amount of spread,
dispersion, or variability of the items in a distribution.

5. Jonnah Mariz Nacar - Bernal
Math Teacher
|| jmgnacar@gmail.com ||
Probability and Statistics
Illustrative Example:
The number of cars sold per day at a local car dealership, along
with its corresponding probabilities, is shown in the succeeding table.
Compute the variance and the standard deviation of the
probability distribution.

6. Jonnah Mariz Nacar - Bernal
Math Teacher
|| jmgnacar@gmail.com ||
Probability and Statistics
Number of cars Probability
P(X)
X ∙ P(X)
0 2
10
1 2
10
2 3
10
3 2
10
4 2
10

7. Jonnah Mariz Nacar - Bernal
Math Teacher
|| jmgnacar@gmail.com ||
Probability and Statistics
1. Find the mean of the probability distribution.
2. Subtract the mean from each value of the random variable X.
3. Square the results obtained in Step 2.
4. Multiply the results obtained in Step 3 by the corresponding
probability.
5. Get the sum of the results obtained in Step 4.
Steps in Finding the Variance and Standard
Deviation of a Discrete Probability Distribution

8. Jonnah Mariz Nacar - Bernal
Math Teacher
|| jmgnacar@gmail.com ||
Probability and Statistics
Number of cars Probability
P(X)
X ∙ P(X)
0 2
10
1 2
10
2 3
10
3 2
10
4 2
10

9. Jonnah Mariz Nacar - Bernal
Math Teacher
|| jmgnacar@gmail.com ||
Probability and Statistics
Scores
X
Number of students
f
X ∙ P(X)
5 3
8 5
10 4
12 5
15 3

10. Jonnah Mariz Nacar - Bernal
Math Teacher
|| jmgnacar@gmail.com ||
Probability and Statistics
ACTIVITY Number of Heads
When three coins are tossed, the probability distribution for the random
variable X representing the number of heads that occur is given below.
Compute the variance and standard deviation of the probability
distribution.

11. Jonnah Mariz Nacar - Bernal
Math Teacher
|| jmgnacar@gmail.com ||
Probability and Statistics
The probabilities of a machine manufacturing Find the variance and
standard deviation of the probability distribution.
Machine
x
Number of
probability
P(X)
X ∙ P(X)
1 0.75
2 0.17
3 0.04
4 0.025
5 0.01

12. Jonnah Mariz Nacar - Bernal
Math Teacher
|| jmgnacar@gmail.com ||
Probability and Statistics
1. Find the mean of the probability distribution.
2. Subtract the mean from each value of the random variable X.
3. Square the results obtained in Step 2.
4. Multiply the results obtained in Step 3 by the corresponding
probability.
5. Get the sum of the results obtained in Step 4.
Steps in Finding the Variance and Standard
Deviation of a Discrete Probability Distribution

13. Jonnah Mariz Nacar - Bernal
Math Teacher
|| jmgnacar@gmail.com ||
Probability and Statistics
Machine
x
Number of
probability
P(X)
X ∙ P(X)
X - 𝝁
(X - 𝝁)𝟐 (X - 𝝁)𝟐∙ P(X)
1 0.75
2 0.17
3 0.04
4 0.025
5 0.01

14. Jonnah Mariz Nacar - Bernal
Math Teacher
|| jmgnacar@gmail.com ||
Probability and Statistics
Finding the Variance and Standard Deviation of a
Discrete Probability Distribution
Alternative Procedure

15. Jonnah Mariz Nacar - Bernal
Math Teacher
|| jmgnacar@gmail.com ||
Probability and Statistics
1. Find the mean of the probability distribution.
2. Multiply the square of the value of the random variable X by its
corresponding probability.
3. Get the sum of the results obtained in Step 2.
4. Subtract the square of the mean from the results obtained in Step 3

16. Jonnah Mariz Nacar - Bernal
Math Teacher
|| jmgnacar@gmail.com ||
Probability and Statistics
x P(X) X ∙ P(X) X2 - 𝝁 (σ X2 - 𝝁) - 𝝁2
1 0.75
2 0.17
3 0.04
4 0.025
5 0.01

17. Jonnah Mariz Nacar - Bernal
Math Teacher
|| jmgnacar@gmail.com ||
Probability and Statistics
The number of inquiries received per day by the Office of Admissions
in a certain university is shown below. Find the variance and standard
deviation.