Suppose first selected number between 1 and 10 is 3,k=10th, find the systematic sample when the population is 50.
A. 3,12,34,45,33
B. 3,13,24,34,36
C. 3,13,23,33,43
D. 3,14,15,34,45

To find the systematic sample, follow these steps:

1. **Identify the first selected number:** Given as 3.
2. **Determine the sampling interval (k):** Given as 10th.
3. **Determine the population size:** Given as 50.

The systematic sample is obtained by adding the sampling interval \( k = 10 \) to the first selected number (3) repeatedly until the maximum population size (50) is reached or exceeded.

Let's calculate the sample:

- Start with 3.
- Add 10: \( 3 + 10 = 13 \)
- Add 10: \( 13 + 10 = 23 \)
- Add 10: \( 23 + 10 = 33 \)
- Add 10: \( 33 + 10 = 43 \)

The systematic sample is \( 3, 13, 23, 33, 43 \).

The correct answer is:

**C. 3,13,23,33,43**

Would you like further details or have any questions?

Here are 8 related questions for practice:

1. What is the systematic sample when the first selected number is 2, \( k = 5 \), and the population size is 30?
2. How do you determine the sampling interval in systematic sampling?
3. What are the advantages of using systematic sampling over simple random sampling?
4. Can systematic sampling introduce bias? Explain why or why not.
5. If the population size is 100, and you choose a first number of 5 with \( k = 15 \), what is the sample?
6. Explain how to choose the first number in systematic sampling.
7. What would the sample be if the first number is 7, \( k = 8 \), and the population size is 40?
8. How does population size affect the number of samples in systematic sampling?

**Tip:** In systematic sampling, ensure the population is not ordered in a way that could introduce bias, as this could affect the randomness of the sample.

Learn how to perform systematic sampling with the given parameters: first selected number 3, sampling interval of 10th, and a population size of 50. Understand the systematic approach to selecting a sample, ensuring accurate representation. Suitable for Grades 10-12 students studying statistics.

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