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The mode is the value that appears most frequently in a data set. In the provided data set, the number 7 appears three times, which is more than any other number. Therefore, the mode of this data set is 7.

3 appears twice, but less frequently than 7.

5 and 10 each appear only once, so they cannot be the mode.

References:

Mode in Statistics - Definition and Examples1

Understanding Measures of Central Tendency2

Mode (statistics) - Wikipedia3

Surveys sent to 100 randomly selected homes that are reflective of the population. This is because a random sample is a type of sample that is selected by using a random method, such as a lottery or a computer-generated number, which ensures that every element in the population has an equal chance of being selected. A random sample can result in a representative sample, which means that the sample reflects the characteristics and diversity of the population. By sending surveys to 100 randomly selected homes that are reflective of the population, the analyst can ensure that the sample is representative of the county’s households and their income levels. The other sampling methodsare not likely to result in a representative sample. Here is why:

A stratified phone survey of 100 people that is conducted between 2:00 p.m. and 3:00 p.m. would result in a biased sample, which means that the sample favors or excludes certain groups or elements in the population. By conducting the survey only between 2:00 p.m. and 3:00 p.m., the analyst would miss out on people who are not available or reachable at that time, such as those who are working or sleeping. This could affect the representativeness and generalizability of the sample.

A systematic survey that is sent to 100 single-family homes in the county would result in an unrepresentative sample, which means that the sample does not reflect the characteristics and diversity of the population. By sending surveys only to single-family homes, the analyst would ignore other types of households, such as apartments, condos, or mobile homes. This could affect the accuracy and reliability of the sample.

Surveys sent to ten randomly selected homes within 5mi (8km) of the county’s office would result in a small sample, which means that the sample size is too low to capture the variability and diversity of the population. By sending surveys only to ten homes within a limited area, the analyst would miss out on many households that are located in different parts of the county. This could affect the precision and confidence of the sample.

Comprehensive and Detailed In-Depth Explanation:

The RefNo column contains values that consist solely of digits without any alphabetical characters or special symbols, indicating a numeric data type.

This is because link analysis is a type of analysis that determines whether the data being analyzed is connected to other datapoints, such as entities, events, or relationships. Link analysis can be used to identify and visualize the patterns, networks, or associations among the datapoints, as well as measure the strength, direction, or frequency of the connections. For example, link analysis can be used to determine if there is a connection between a customer’s purchase history and their loyalty program status. The other types of analysis are not the best types of analysis to conduct to determine whether the data being analyzed is connected to other datapoints. Here is why:

Trend analysis is a type of analysis that determines whether the data being analyzed is changing over time, such as increasing, decreasing, or fluctuating. Trend analysis can be used to identify and visualize the patterns, cycles, or movements in the data points, as well as measure the rate, direction, or magnitude of the changes. For example, trend analysis can be used to determine if there is a change in a company’s sales revenue over a period of time.

Performance analysis is a type of analysis that determines whether the data being analyzed is meeting certain goals or objectives, such as targets, benchmarks, or standards. Performance analysis can be used to identify and visualize the gaps, deviations, or variations in the data points, as well as measure the efficiency, effectiveness, or quality of the outcomes. For example, performance analysis can be used to determine if there is a gap between a student’s test score and their expected score based on their previous performance.

Exploratory analysis is a type of analysis that determines whether there are any insights or discoveries in the data being analyzed, such as patterns, relationships, or anomalies. Exploratory analysis can be used to identify and visualize the characteristics, features, or behaviors of the data points, as well as measure their distribution, frequency, or correlation. For example, exploratory analysis can be used to determine if there are any outliers or unusual values in a dataset.