A numerical summary of a population is a
A Parameter
B Statistic
C Variable
D Qualitative response
The correct answer and explanation is:
The correct answer is A. Parameter.
A parameter is a numerical summary that describes a characteristic of a population. In statistics, a population refers to the entire group of individuals or items that are being studied, and the parameter provides a fixed measure of a feature of that group. For instance, the average height of all people in a country, or the total income of all households in a city, are examples of parameters because they describe the entire population.
On the other hand, a statistic is a numerical summary of a sample, which is a subset of the population. The statistic is used to estimate the corresponding parameter, but it is subject to sampling variability, meaning it can change depending on the sample selected. For example, the average height calculated from a random sample of 100 people would be a statistic.
A variable refers to any characteristic or attribute that can take on different values. Variables can be quantitative (e.g., age, height, income) or qualitative (e.g., gender, color, type of disease). These values can vary between individuals in a population or a sample.
A qualitative response refers to data that can be categorized or classified, such as color, type, or category of a product. Qualitative data does not involve numerical measurements but rather labels or categories.
To sum up, while parameters describe a population, statistics describe a sample. The distinction is crucial for understanding how data is collected, analyzed, and used for decision-making, as well as in the process of making inferences about the population based on sample data.