To draw a simple random sample of size 5 without replacement from a population of 220 students (Roll Nos. from 1 to 220) using a random number series table, follow these steps:

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Step-by-Step Procedure

1. Assign Numbers to the Population: Each student is assigned a unique Roll Number from 1 to 220.

2. Determine the Number of Digits Required: Since the population size is 220, three-digit numbers will be used to represent each student (e.g., Roll No. 001 to Roll No. 220).

3. Use the Random Number Table:

   • Open a random number table and begin at a random starting point. For example, choose a starting row and column arbitrarily or randomly.
   • Read numbers in groups of three digits to match the Roll Numbers (e.g., "045," "173").
   • Skip any three-digit number greater than 220 or duplicates to ensure uniqueness.

4. Select Numbers:

   • Continue reading until you select exactly 5 distinct numbers corresponding to Roll Numbers.
   • For example, if the random number table gives: 045, 173, 015, 088, 200, these are the selected Roll Numbers.

5. Identify Students:

   • The Roll Numbers selected correspond to the students in the sample.
   • If the selected numbers represent Roll Nos. 45, 173, 15, 88, and 200, these students form the random sample.

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Example Using a Random Number Table

Suppose the table provides the following sequence of three-digit numbers starting from a random location:

145 045 245 173 088 200 290 015 088 312

From this sequence:

• 145: Valid, within 1–220.
• 045: Valid, within 1–220.
• 245: Invalid, exceeds 220.
• 173: Valid, within 1–220.
• 088: Valid, within 1–220.
• 200: Valid, within 1–220.

Thus, the selected Roll Numbers are 145, 045, 173, 088, 200.

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Key Points:

• The selection is random and unbiased.
• No repetition or replacement occurs; once a number is chosen, it is excluded from further consideration.
• Numbers exceeding 220 or duplicates are ignored.

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Would you like me to explain more or simulate a random sampling process? Here are some related questions:

1. What are the advantages of using a random sampling number series table?
2. How does simple random sampling differ from systematic sampling?
3. Can this method be automated using programming tools like Python?
4. What challenges arise in manual random number table usage for large populations?
5. Why is sampling without replacement more common in finite populations?

Tip: Always verify the randomness and ensure that no bias occurs during the selection process!