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Answer :
To determine which option represents a possible cluster sample of homes in the city, let's first remember what a cluster sample is. In cluster sampling, the population is divided into naturally occurring groups called clusters. A random selection of clusters is then chosen, and either all members of the selected clusters are surveyed, or a random selection of members from those clusters is taken.
Let's examine the options provided:
Option A:
1326, 1325, 1593, 1627, 1474, 6581, 8845, 8125
- These house numbers are from various different blocks and not all from a single block. This does not represent a cluster sample.
Option B:
7349, 7352, 7353, 7356, 7357, 7360, 7361, 7364
- These house numbers all come from the same block. Hence, they represent a cluster sample, as they are all grouped together in a specific part of the city.
Option C:
1473, 1624, 1329, 8845, 1477, 7356, 1592, 1592
- Similar to Option A, these house numbers are spread across different blocks. This does not represent a cluster sample.
Option D:
6589, 1476, 1626, 7360, 8842, 8134, 1326, 1594
- Again, these house numbers are from various parts of the city and not from a single cluster. This is also not a cluster sample.
From the analysis, we can see that Option B is the only one where all house numbers are from the same block. Therefore, it correctly represents a possible cluster sample.
The correct answer is:
B. 7349, 7352, 7353, 7356, 7357, 7360, 7361, 7364
Let's examine the options provided:
Option A:
1326, 1325, 1593, 1627, 1474, 6581, 8845, 8125
- These house numbers are from various different blocks and not all from a single block. This does not represent a cluster sample.
Option B:
7349, 7352, 7353, 7356, 7357, 7360, 7361, 7364
- These house numbers all come from the same block. Hence, they represent a cluster sample, as they are all grouped together in a specific part of the city.
Option C:
1473, 1624, 1329, 8845, 1477, 7356, 1592, 1592
- Similar to Option A, these house numbers are spread across different blocks. This does not represent a cluster sample.
Option D:
6589, 1476, 1626, 7360, 8842, 8134, 1326, 1594
- Again, these house numbers are from various parts of the city and not from a single cluster. This is also not a cluster sample.
From the analysis, we can see that Option B is the only one where all house numbers are from the same block. Therefore, it correctly represents a possible cluster sample.
The correct answer is:
B. 7349, 7352, 7353, 7356, 7357, 7360, 7361, 7364
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Rewritten by : Barada
To solve this problem, we need to understand what a cluster sample is and then identify which option reflects a cluster sample.
Cluster Sampling Explained:
- Cluster sampling is a method where the population is divided into separate groups, known as clusters.
- In a cluster sample, the entire cluster is chosen randomly, and every house within that selected cluster is surveyed or used in the sample.
Identification of Clusters:
- In this context, each block of numbers can represent a cluster. For example, all house numbers in the range from 7349 to 7364 form a single distinct cluster.
Analysis of the Options:
Option A: $1326, 1325, 1593, 1627, 1474, 6581, 8845, 8125$
- This option is not a cluster sample because it picks individual houses randomly from different blocks, not an entire cluster.
Option B: $7349, 7352, 7353, 7356, 7357, 7360, 7361, 7364$
- This option represents a cluster sample as it includes all houses within one block (7349 to 7364), effectively sampling the entire cluster.
Option C: $1473, 1624, 1329, 8845, 1477, 7356, 1592, 1592$
- This is not a cluster sample because it similarly picks houses from various unrelated blocks.
Option D: $6589, 1476, 1626, 7360, 8842, 8134, 1326, 1594$
- This also does not represent a cluster sample as it involves houses from different blocks.
Conclusion:
- Option B correctly represents a cluster sample as it samples all of the houses from the single block containing addresses from 7349 to 7364.
Therefore, the correct choice is Option B.
Missing Table from question added below:
