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### Sampling.pptx

1. Statistics and Probability Pauline Misty M. Panganiban SAMPLING DISTRIBUTION OF SAMPLE MEANS
2. L i b e r a t i n g N e t w o r k i n E d u c a t i o n illustrate random sampling; distinguish between parameter and statistic; and construct sampling distribution of sample means. Objectives
3. L i b e r a t i n g N e t w o r k i n E d u c a t i o n Constructing Frequency Distribution The following are the blood types of a group of individuals in a government office. Construct a frequency distribution for the different blood types
4. L i b e r a t i n g N e t w o r k i n E d u c a t i o n Constructing Frequency Distribution x f A 5 B 7 O 9 AB 4
5. L i b e r a t i n g N e t w o r k i n E d u c a t i o n •You have learned in your previous lessons how to construct frequency distribution and probability distribution. In this lesson, you will learn how to construct sampling distribution of the sample means.
6. L i b e r a t i n g N e t w o r k i n E d u c a t i o n Computing for the mean of a Sample Find the mean of the following sets numbers
7. L i b e r a t i n g N e t w o r k i n E d u c a t i o n Combination A combination is a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter. In combinations, you can select the items in any order.
8. L i b e r a t i n g N e t w o r k i n E d u c a t i o n Combination of N objects Taken r at a time. The number of samples of size r that can be drawn from a population of size N is given by NCn. 𝑛𝐶𝑟 = 𝑛! 𝑟!(𝑛−𝑟)! Where: n = size of the population r = size of the sample
9. L i b e r a t i n g N e t w o r k i n E d u c a t i o n Evaluating Combination of N objects Taken n at a time. 1. 4C2 2. 6C4 3. 6C3 4. 10C4 = 𝑁! 𝑛!(𝑁−𝑛)! = 4! 2!(4−2)! = 4! 2!(2)! = 4 3 2! 2!2! = 12 2 = 𝟔 = 𝑁! 𝑛!(𝑁−𝑛)! = 6! 4!(6−4)! = 6! 4!(2)! = 6(5)(4!) 4!2! = 30 2 = 𝟏𝟓 = 𝑁! 𝑛!(𝑁−𝑛)! = 6! 3!(6−3)! = 6! 3!(3)! = 6(5)(4)(3!) 3!3! = 6 5 (4) 3(2)(1) = 𝟐𝟎 = 𝑁! 𝑛!(𝑁−𝑛)! = 10! 4!(10−4)! = 10! 4!(6)! = 10(9)(8)(7)(6!) 4!6! = 10(9)(8)(7) 4(3)(2)(1) = 𝟐𝟏𝟎
10. L i b e r a t i n g N e t w o r k i n E d u c a t i o n Evaluate the following. 1. 5𝐶3 2. 8𝐶4 3. 9𝐶6 4. 10𝐶3 5. 12𝐶8
11. L i b e r a t i n g N e t w o r k i n E d u c a t i o n •Researchers use sampling if taking a census of the entire population is impractical. Data from the sample are used to calculate statistics, which are estimates of the corresponding population parameters.
12. L i b e r a t i n g N e t w o r k i n E d u c a t i o n •Descriptive measures computed from a population.
13. L i b e r a t i n g N e t w o r k i n E d u c a t i o n •Descriptive measures computed from a sample.
14. L i b e r a t i n g N e t w o r k i n E d u c a t i o n Sampling Distribution of Sample Means • The number of samples of size r that can be drawn from a population of size N is given by NCr. • A sampling distribution of sample means is a frequency distribution using the means computed from all possible random samples of a specific size taken from a population. • The probability distribution of the sample means is also called the sampling distribution of the sample means.
15. L i b e r a t i n g N e t w o r k i n E d u c a t i o n Steps in Constructing the Sampling Distribution of the Means 1. Determine the number of possible samples that can be drawn from the population using the formula: NCr where N = size of the population r = size of the sample 2. List all the possible samples and compute the mean of each sample. 3. Construct a frequency distribution of the sample means obtained in Step 2.
16. L i b e r a t i n g N e t w o r k i n E d u c a t i o n Example A population consists of the numbers 2, 4, 9, 10, and 5. a. List all possible samples of size 3 from this population. b.Compute the mean of each sample. c. Prepare a sampling distribution of the sample means.
17. L i b e r a t i n g N e t w o r k i n E d u c a t i o n Solution to Example 1a The possible samples of size 3 from 2, 4, 9, 10, and 5 are…
18. L i b e r a t i n g N e t w o r k i n E d u c a t i o n Solution to Example 1b The mean of each sample are as follows:
19. L i b e r a t i n g N e t w o r k i n E d u c a t i o n Solution to Example 1c The sampling distribution of the sample means
20. L i b e r a t i n g N e t w o r k i n E d u c a t i o n Exercise A group of students got the following scores in a test: 6, 9, 12, 15, 18, and 21. Consider samples of size 3 that can be drawn from this population. a. List all the possible samples and the corresponding mean. b. Construct the sampling distribution of the sample means.
21. L i b e r a t i n g N e t w o r k i n E d u c a t i o n Exercise 1 Samples of three cards are drawn at random from a population of eight cards numbered from 1 to 8. a. How many possible samples can be drawn? b.Construct the sampling distribution of sample means.
22. L i b e r a t i n g N e t w o r k i n E d u c a t i o n Exercise 3 A finite population consists of 8 elements. 10, 10, 10, 10, 10, 12, 18, 40 a. How many samples of size n = 2 can be drawn from this population? b. List all the possible samples and the corresponding means. c. Construct the sampling distribution of the sample means.
23. L i b e r a t i n g N e t w o r k i n E d u c a t i o n Thank you!

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