STATISTICS & PROBABILITY-calculating the variance and standard deviation.pptx

this is a presentation for statistics and probability, Quarter 3. The lesson is about calculating the variance and standard deviation

1. STATISTICS & PROBABILITY JAY VEE Q. GARALDE Teacher I

2. Mean and Variance of Discrete Random Variable

3. Calculate the mean and the variance of a discrete random variable; Interpret the mean and the variance of a discrete random variable; and OBJECTIVES

4. What is the word? VAEGERA AVERAGE

5. What is the word? MAEN MEAN

6. What is the word? STNAARD DVEAINIOT STANDARD DEVIATION

7. What is the word? RNAODM AVRIAELB RANDOM VARIABLE

8. What is the word? AVIARECN VARIANCE

9. Mean of the Discrete Random Variable Covid-19 is continuously spreading around the world, that is why reports regarding average infected people per country is being updated every day. For this kind of report, experts used Statistics and Probability to show reliable analysis in their data. In this lesson, you will learn how to compute the average or mean of a discrete probability distribution as well as the variance and standard deviation of a discrete random variable.

10. How can we describe the spread or dispersion in a probability distribution?

11. Variance and Standard Deviation of the Discrete Random Variable The variance and standard deviation describe the amount of spread, dispersion, or variability of the items in a distribution. How can we describe the spread or dispersion in a probability distribution? In this lesson, you will learn how to compute the variance and standard deviation of a discrete probability distribution. Now, let us find out how can we find the variance and standard deviation of a discrete probability distribution.

12. What’s New Variance and Standard Deviation of a Random Variable The variance and standard deviation are two values that describe how scattered or spread out the scores are from the mean value of the random variable. The variance, denoted as σ 2 , is determined using the formula: σ 2 = ∑( x − µ) 2 p(x) The standard deviation σ is the square root of the variance, thus, σ = √ ∑( x − µ)² p (x ) σ 2 - variance σ – standard deviation µ - mean p(x) – probability of the outcome

13. What is It Let’s try! Let’s have examples: 1. 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 by following the given steps. Write your answer in your answer sheets. Number of Cars Sold X Probability P(x) 10% 1 20% 2 30% 3 20% 4 20%

14. In solving the problem, let’s follow the steps below. STEPS IN FINDING THE VARIANCE AND STANDARD DEVIATION 1. Find the mean of the probability distribution. 2. Subtract the mean from each value of the random variable X. 3. Square the result 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. Results obtained is the value of the variance of probability distribution.

15. Now let’s solve the problem.

16. Continuation

17. To Solve for Standard Deviation: Get the square root of the variance σ 2 = ∑( x − µ) 2 p(x) = 1.56 σ = √1.56 = 1.25 So, the variance of the number of cars sold per day is 1.56 and the standard deviation is 1.25.

18. 2. When three coins are tossed once, 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. Solution: Follow the steps in finding variance and standard deviation of the probability distribution.

19. To solve for Standard Deviation σ 2 = ∑( x − µ) 2 p(x) = 0.74 σ = √0.74 = 0.86 The mean in tossing 3 coins with probability of Head will show up is 0.86 and the variance is 0.74, then the standard deviation is 0.86.

20. What’s More Determine the Variance and Standard Deviation of each random variable. Write your answer in your answer sheets. P(x) 1 5 1 5 1 5 1 5 1 5

21. Answer the following questions in your own understanding. 1. How to compute the mean of a discrete random variable? State the 3 steps. Write your answer in your answer sheets. 2. How to find the variance and standard deviation of a discrete random variable? Write your answer in your answer sheets. What I Have Learned

22. Assessment Find the mean, variance , and standard deviation of the following probability distribution then interpret the computed values. 1. Variable z representing the number of male teachers per Elementary school. 2. The number of mobile phones sold per day at a retail store varies as shown in the given probability distribution below. Find the expected number of mobile phones that will be sold in one day. z 2 3 4 5 6 P(z) 40% 32% 11% 9% 8% x 30 33 38 40 50 P(x) 0.2 0.2 0.35 0.23 0.02

23. What I Can Do Make a study about how many sheets of paper you consumed weekly in answering your Self Learning Modules. Record the quantity (total number of sheets) per subject, then construct a probability distribution. Compute the mean, variance, and the standard deviation of the probability distribution you made. Interpret the result, then find out how many weeks you will consume 50 sheets of pad paper.

24. THANK YOU!