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Chapter 1: Problem 8

Determine whether the underlined value is a parameter or a statistic. The average score for a class of 28 students taking a calculus midterm exam was \(72 \%\).

Short Answer

Expert verified
The underlined value (72%) is a parameter because it describes an entire population (the class of 28 students).

Step by step solution

01

Understand the Context

Determine whether the value given (72%) pertains to a sample or an entire population. A parameter describes an entire population, while a statistic describes a sample.
02

Identify the Group

Notice that the problem states the average score for a class of 28 students. Since it mentions the entire class, it implies the entire group concerned with the measurement.
03

Determine the Value Type

Given that the average score is for all 28 students in the class, this measurement describes the entire population of that class. Hence, it is a parameter.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Population
In statistics, a population refers to the entire group of individuals or items that you are interested in studying. It can be as large as all the people in a country or as small as all the students in a particular classroom.
In the context of our exercise, the population is the entire class of 28 students taking the calculus midterm exam. This means the average score of 72% pertains to all members of this group.
When we talk about a population, we often use the term 'parameter' to describe a characteristic or measure that summarizes the entire group. In our example, since we are considering the whole class, the average score is a parameter.
Sample
A sample is a smaller group selected from the population. It is used when it's impractical or impossible to study the entire population. For example, if we wanted to study student performance in calculus across an entire university, we might select a sample of students from different classes rather than surveying every single student.
In our exercise, if we had only considered the average score of a few students, then that measure would be termed a statistic.
This distinction is crucial for statistical analysis since a sample may not represent the full diversity of the population, leading to potential biases in the conclusions drawn.
Average Score
The average score, also known as the mean, is a measure that summarizes a set of values. It is calculated by adding up all the values and then dividing by the number of values.
In our exercise, the average score of 72% was obtained by adding up all the scores of the 28 students and dividing by 28. This gives us a single number that summarizes the group's performance.
The average score is a useful measure because it provides a central value around which the individual scores are distributed, giving us a quick glimpse of the overall performance of the group.

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