Grade 11 – Statistics and Probability
LEARNING ACTIVITY SHEET (LAS)
Name:
Date:
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ACTIVITY I
RANDOM VARIABLES AND PROBABILITY DISTRIBUTIONS
A. Directions: Determine whether the items are discrete or continuous random variables. Write D if the
random variable is discrete, and C if it is continuous.
__________ 1.
__________ 2.
__________ 3.
__________ 4.
__________ 5.
__________ 6.
__________ 7.
__________ 8.
__________ 9.
__________ 10.
The temperature in Taguig City
The weight of each student in the class
The scores of students in a 25-item test
The number of students present in the class
The amount of money earned in an investment
The number of students admitted in a certain school
The family income of the students in a certain school
The distance travelled of the students in going to school.
The length of TV commercial (in seconds) from 8:00 PM – 11:00 PM
The waiting time of the customers to receive their orders from online shopping
B. Directions: Modified True or False. Write T if the statement is correct; indicate the appropriate answer
by changing the underlined word or phrase otherwise.
__________ 1. The discrete random variables are random variables whose values are obtained by
measuring.
__________ 2. The probability of each value of discrete random variable is between 0 and 1
exclusively.
__________ 3. The sum of all the probabilities of a discrete random variable is equal to one.
__________ 4.
A random variable is a numerical description of an outcome in an experiment.
__________ 5.
The values of a continuous random variables are in ratio.
C. Directions: Find the random variable and its probabilities for each given item. Construct a probability
distribution. Use the provided table for the random variables and its probabilities and the box for the
probability distribution.
1. In a file of 10 records with 2 errors, 5 are examined. Let the random variable 𝑋 be the number of errors.
𝑋
𝑃(𝑋)
Specific Week: Week 1 to Week 3
Target Competencies: Illustrate the random variable (discrete and continuous), Distinguish between a discrete and a continuous random variable, Find the
possible values of a random variable, illustrate a probability distribution for a discrete random variable and its properties and Compute probabilities to a given
random variable.
Grade 11 – Statistics and Probability
LEARNING ACTIVITY SHEET (LAS)
2. Three paper bills are drawn in succession without replacement from a piggy bank containing 10 20peso bill, 15 50-peso bill, and 5 100-peso bill. Let random variable X be the number of 20-peso bill
drawn.
𝑋
𝑃(𝑋)
THINK MORE! In which aspects of your life can you associate the ideas of discrete
random variables and continuous random variables? Illustrate the importance of these
two variables in dealing with the circumstances you encounter in your everyday life.
Activity II
MEAN, VARIANCE, AND STANDARD DEVIATION OF A
DISCRETE PROBABILITY DISTRIBUTION
A. Directions: Complete the table below, then find the mean, variance, and the standard deviation of the
following probability distribution. Write your answers on the space provided.
1.
𝑋
0
1
2
3
𝑃(𝑋)
𝑋 ∙ 𝑃(𝑋)
𝑋−𝜇
(𝑋 − 𝜇)2
(𝑋 − 𝜇)2 ∙ 𝑃(𝑋)
1
5
2
5
3
10
1
10
What is mean of the probability distribution?
What is variance of the probability distribution?
What is the standard deviation of the probability distribution?
Specific Week: Week 1 to Week 3
Target Competencies: Illustrate the random variable (discrete and continuous), Distinguish between a discrete and a continuous random variable, Find the
possible values of a random variable, illustrate a probability distribution for a discrete random variable and its properties and Compute probabilities to a given
random variable.
Grade 11 – Statistics and Probability
LEARNING ACTIVITY SHEET (LAS)
2.
𝑋
𝑃(𝑋)
2
0.50
8
0.30
10
0.20
𝑋 ∙ 𝑃(𝑋)
(𝑋 − 𝜇)2
𝑋−𝜇
(𝑋 − 𝜇)2 ∙ 𝑃(𝑋)
What is mean of the probability distribution?
What is variance of the probability distribution?
What is the standard deviation of the probability distribution?
B. Directions: Solve the following problems. Write your final answer inside the box.
1. An investment will be worth PHP 1,000, PHP 2,000, or PHP 5,000 at the end of the year. The
probabilities of these values are 0.25, 0.60 and 0.15, respectively. Find the mean, variance, and the
standard deviation of the worth of the investment.
𝑋
Mean
𝑃(𝑋)
𝑋 ∙ 𝑃(𝑋)
𝑋−𝜇
Variance
(𝑋 − 𝜇)2
(𝑋 − 𝜇)2
∙ 𝑃(𝑋)
Standard Deviation
2. Jonathan sells new cars. Jonathan usually sells the largest number of cars on Wednesdays. He has
developed the following probability distribution for the number of cars he expects to sell on a particular
Wednesday. Find the mean, variance, and standard deviation of the probability distribution.
Number of Cars Sold,
𝑋
0
1
2
3
4
Probability
𝑃(𝑋)
0.10
0.20
0.30
0.30
0.10
Random Variables and Probability Distributions
Third Quarter Week 1 to Week 3
Target Competency:
Illustrate the mean and variance of a discrete random variable.
Calculate the mean and the variance of a discrete random variable.
Interpret the mean and the variance of a discrete random variable.
Solve problems involving the mean and the variance of probability distributions.
Grade 11 – Statistics and Probability
LEARNING ACTIVITY SHEET (LAS)
𝑋
𝑃(𝑋)
Mean
𝑋 ∙ 𝑃(𝑋)
Variance
𝑋−𝜇
(𝑋 − 𝜇)2
(𝑋 − 𝜇)2 ∙ 𝑃(𝑋)
Standard Deviation
THINK MORE! How would you compare the two groups of students that have the
same mean values but different variances? In life, what standards do you use to say
that any two given groups are similar or different?
Random Variables and Probability Distributions
Third Quarter Week 1 to Week 3
Target Competency:
Illustrate the mean and variance of a discrete random variable.
Calculate the mean and the variance of a discrete random variable.
Interpret the mean and the variance of a discrete random variable.
Solve problems involving the mean and the variance of probability distributions.
Activity I
A.
1. C
2. C
3. D
4. D
5. C
6. D
7. C
8. C
9. C
10. C
B.
1. counting
2. inclusively
3. T
4. T
5. Interval
C.
1.
𝑋
𝑃(𝑋)
2
9
2
5
9
1
2
9
0
Statistics and Probability
Grade 11
Third Quarter
Learning Activity Sheet (LAS)
Activity II
A.
1.
𝑋
0
1
2
3
𝑃(𝑋)
1
5
2
5
3
10
1
10
13
𝑋 ∙ 𝑃(𝑋)
0
2
5
3
5
3
10
𝑋−𝜇
−1.30
−0.30
0.70
1.70
(𝑋 − 𝜇)2
(𝑋 − 𝜇)2 ∙ 𝑃(𝑋)
0.338
1.69
0.036
0.09
0.147
0.49
0.289
2.89
Mean =10 or 1.30
Variance = 0.81
Standard Deviation = 0.9
2.
1
0.50
2
𝑋 ∙ 𝑃(𝑋)
𝑃(𝑋)
𝑋
0.20
10
0.30
8
2.4
2
𝑋−𝜇
−3.4
2.6
4.6
(𝑋 − 𝜇)2
11.56
6.76
21.16
(𝑋 − 𝜇)2 ∙ 𝑃(𝑋)
5.78
2.028
4.232
Mean = 5.4
Variance = 12.04
Standard Deviation = 3.47
B.
1.
250
0.25
1, 000
𝑋 ∙ 𝑃(𝑋)
𝑃(𝑋)
𝑋
0.15
5,000
0.60
2,000
1200
750
𝑋−𝜇
−1200
−200
2800
(𝑋 − 𝜇)2
1,440,000
40,000
7,840,000
(𝑋 − 𝜇)2 ∙ 𝑃(𝑋)
360,000
24,000
1,176,000
Mean = 2,200
Variance = 1,560,000
Standard Deviation = 1,249
2.
2.
𝑋
𝑃(𝑋)
6
203
3
45
203
2
95
203
1
57
203
0
0.30
3
0.30
2
0.20
1
−2.10
0.00
0.10
0
𝑋−𝜇
𝑋 ∙ 𝑃(𝑋)
𝑃(𝑋)
𝑋
4
0.20
0.60
0.90
0.10
0.40
−1.10
−0.10
0.90
1.90
(𝑋 − 𝜇)2
4.41
1.21
0.01
0.81
3.61
(𝑋 − 𝜇)2 ∙ 𝑃(𝑋)
0.441
0.242
0.003
0.243
0.361
Mean = 2.10
Variance = 1.29
Standard Deviation = 1.13578
LEARNING ACTIVITY SHEET (LAS)
Grade 11 – Statistics and Probability