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Sampling methods — Statistics STD 11 Commerce — Question

Gujarat BoardEnglish MediumSTD 11 CommerceStatisticsSampling methods4 Marks
Question
For studying the usage of mobile phones, randomly select $7$ persons without replacement from $30$ boys and $20$ girls from a locality of a city. There should be $3$ boys and $4$ girls in the randomly selected $7$ persons.
Random numbers for boys : $82, 95, 18, 96, 20, 84, 56, 11, 52, 03$
Random numbers for girls : $04, 40, 34, 13, 72, 11, 50, 55, 08, 11, 76, 18$
✓

Answer

We shall first divide $50$ persons into two groups (strata) Boys and Girls. Now we will select a random sample of $3$ boys from $30$ boys and $4$ girls from $20$ girls using simple random sampling method.Selecting sample of size $3$ from $30$ boys :
Numbers $1$ to $30$ will be assigned to $30$ boys. Since there are $30$ boys, we shall ignore random numbers which are greater than $30$. As the sample has to be selected without replacement, we shall also ignore the random numbers which are repeated more than once. We require a random sample of size $3$, so we shall select first $3$ random numbers. Thus, the selected random numbers are: $18, 20$ and $11$. Boys with these numbers are selected from all boys of the locality.
Selecting sample of size $4$ from $20$ girls :
Numbers $1$ to $20$ will be assigned to $20$ girls. Since there are $20$ girls, we shall ignore random numbers which are greater than $20$. As the sample has to be selected without replacement, we shall also ignore the random numbers which are repeated more than once. We require a random sample of size $4$, so we shall select first $4$ random numbers. Thus, the selected random numbers are: $04, 13, 11$ and $8$. Girls with these numbers are selected from all girls of the locality.
Stratified random sample of size $7$ is the combination of these selected $3$ boys and $4$ girls.

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