2 Mark Each

Question 12 Marks

Select all possible systematic samples of size $3$ from a population of size $12.$

Answer

Here population size $(N)$ is $12$ and sample size $(n) = 3$.
So the sample interval $k = N/n = 12/3 = 4.$
Now, every 4th unit will be selected after randomly selecting the first unit from $1$ to $4.$ Thus we will get $4$ possible samples.

Thus, possible samples are:
Sample $I : 1, 5, 9$
Sample $II : 2, 6, 10$
Sample $III : 3, 7, 11$
Sample $IV : 4, 8, 12$

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Question 22 Marks

An owner of a service station has a list of $1000$ car owners who have got their car repaired at his service station. He wishes to conduct satisfaction survey of $50$ car owners. Explain how a sample of $50$ car owners can be selected using systematic sampling.

Answer

Here, total number of car owners is $1000$ i.e. $N = 1000$ and we have to select $50$ car owners i.e. $n = 50.$ So, the sample interval $k = N/n = 1000/50 = 20.$
Now, every $20th$ car owner will be selected after randomly selecting one car owner from $1$ to $20.$
Suppose car owner number $11$ is selected from ﬁrst $20$ car owners then the car owners with following numbers will be selected in systematic sample for conducting satisfaction survey $11, 31, 51, 71, ...., 991.$

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Question 32 Marks

There are $40$ ﬂats in a multi—storied apartment. $5$ ﬂats are to be selected using systematic sampling from $40$ ﬂats for decoration in a cultural program. Explain how the sample can be selected ?

Answer

Here, total number of ﬂats is $40$ i.e. $N = 40$ and we have to select $5$ ﬂats i.e. $n = 5.$
So, the sampling interval $k = N/n = 40/5 = 8$.
Now, every 8th ﬂat will be selected after randomly selecting one ﬂat from ﬂat number $1$ to $8$.
Suppose ﬂat number $3$ is selected from ﬁrst $8$ ﬂats then ﬂats with following numbers are selected:
$3,11,19,27,35.$

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Question 42 Marks

Define stratum in stratified random sampling.

Answer

In stratified random sampling the groups obtained due to stratification which differ from one another but internally they are almost same in terms of variation. Each of such strata is called stratum.

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Question 52 Marks

Explain the process of stratification.

Answer

A process of dividing heterogeneous, population into non - overlapping fairly homogeneous groups is called stratification and these groups are called strata.

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Question 62 Marks

Explain sample interval in systematic random sampling.

Answer

The ratio of population size $N$ and sample size n is called sample interval in systematic sampling. It is denoted by $k$ which is a positive integer and defined as $k=\frac{ N }{ n }$.

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Question 72 Marks

State the strategies used for deciding the number of units to be selected from each stratum in stratified random sampling.

Answer

In stratified random sampling. a sample is drawn from each stratum by selecting the units at random in proportion to the size of each stratum.

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Question 82 Marks

Name various methods of sampling.

Answer

The various methods of sampling are : $(1)$ Simple random sampling, $(2)$ Stratified random sampling and $(3)$ Systematic sampling.

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Question 92 Marks

State the methods of selecting a simple random sample.

Answer

Two methods of selecting a simple random sample are : $(1)$ Method of lottery and $(2)$ Method of random number table.

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Question 102 Marks

What is sampling ?

Answer

The procedure of selecting a sample from a population is called sampling.

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Question 112 Marks

When is sample inquiry undertaken ?

Answer

Sample inquiry is undertaken in following circumstances :
$(1)$ The units in a population is very large.
$(2)$ The population is spread over wide geographical area.
$(3)$The units under inquiry are to be destroyed during the inspection.
$(4)$ The availability of time, money and expertise for conducting an inquiry is limited.

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