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Sampling methods · Gujarat Board (GSEB) STD 11 Commerce (GSEB - English Medium). 6 questions.

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Question 13 Marks
A fruit merchant wants to send $10$ boxes of apples out of $40$ boxes to his relatives. Obtain all possible samples using systematic sampling.
Answer
$N =40, n=10, k=\frac{ N }{n}=\frac{40}{10}=4$
$\text { Sample I : } 1, 5, 9, 13, 17, 21, 25, 29, 33, 37 $
$\text{ Sample II : } 2, 6, 10, 14, 18, 22, 26, 30, 34, 38 $
$\text { Sample III : } 3, 7, 11, 15, 19, 23, 27, 31, 35, 39 $
$ \text { Sample IV : } 4, 8, 12, 16, 20, 24, 28, 32, 36, 40$
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Question 33 Marks
Some youth are participating in cricket coaching in a club. Among them, $60$ youth are $15$ to $25$ years old and $40$ youth are $25$ to $35$ years old. Obtain a sample without replacement from this population using stratified sampling by selecting $7$ youth of age $15$ to $25$ years and $4$ of age $25$ to $35$ years.
Random numbers for $15$ to $25$ years old youth :
$40,25,80,39,19,27,18,25,79,19,58,24,25,34,22,27,21,26,29$
Random numbers for $25$ to $35$ years old youth :
$51,33,38,35,45,41,33,57,28,32,36,28$
Answer
Sample without replacement of youth from $15$ to $25$ years : $40, 25, 39, 19, 27, 18, 58$
Sample without replacement of youth from $25$ to $35$ years : $33,38,35,28$
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Question 43 Marks
Three digit random number are given below. Select a $2 \%$ random sample with and without replacement from a population of size $500$ using these random numbers.$270,530,390,420,270,111,189,273,692,488,512,192,219,912,129,723$
Answer
$N =500, n=10$
Sample without replacement $: \quad 270,390,420,111,189,273,488,192,219,129$
Sample with replacement $: \quad 270,390,420,270,111,189,273,488,192,219$
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3 Marks Each - Statistics STD 11 Commerce Questions - Vidyadip