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Chapter 5: Problem 17

For Exercises 13 through 18, state whether the variable is discrete or continuous. The total number of points scored in a basketball game

Short Answer

Expert verified
The variable is discrete.

Step by step solution

01

Understanding the Problem

To determine whether a variable is discrete or continuous, we need to understand what these terms mean. A discrete variable is one that has specific, separate values, often counts of things, while a continuous variable can take any value within a range, often measurements.
02

Identify the Variable

The variable we are examining is the total number of points scored in a basketball game. Points in a game are determined by scoring specific actions such as free throws, 2-pointers, and 3-pointers.
03

Determine if the Variable is Countable

Since each point in basketball is an indivisible whole number (e.g., 1, 2, 3), we can count them in increments of whole numbers. Thus, the total score can be listed as a series of whole numbers.
04

Classify the Variable

As the total number of points in a game is countable in whole numbers and does not take on fractional values, it fits the definition of a discrete variable. Each point is a distinct, countable entity.

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Key Concepts

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

Discrete Variable
In statistics, a discrete variable represents countable items and is characterized by distinct and separate values. Such variables encompass data that can be counted in whole units, without any possibility of fractions or decimals. Suppose you consider something like the number of books on a shelf鈥攖hose books can only exist in whole numbers, not partial ones, making it a discrete variable. Some characteristics of discrete variables include:
  • Individual values are distinct and separate.
  • Values are countable and finite.
  • No intermediate values exist between adjacent countable values.
Understanding discrete variables is important because it helps in choosing the right statistical analyses and graphical representations for your data. For example, a bar chart is ideal for displaying discrete data.
Continuous Variable
Continuous variables are those that can take any value within a specified range. Unlike discrete variables, continuous variables are all about measurements rather than counts. This means they can have infinitely many possible values that are not restricted to specific, separate values. Imagine measuring the height of a person. Someone could be 5.8 feet, 5.81 feet, or 5.812 feet tall. This kind of variable allows for fractional numbers and is thus called continuous. Key traits of continuous variables include:
  • Values fall within an infinite range.
  • They can assume any value between two numbers (fractions, decimals).
  • Depth of detail is greater as they offer a range of possibilities.
Continuous variables are best represented using line graphs or histograms, which can show the distribution of the variable across a range.
Data Classification
Classifying data correctly is a fundamental step in statistical analysis. When data are well classified, it improves understanding, insights, and decision-making. Data can be classified into qualitative and quantitative types.
  • Qualitative data: These data represent categories or attributes and are often collected as labels or names. Examples include colors, types of movies, or genres of music.
  • Quantitative data: This type deals with numbers and amounts鈥攙alues that can be measured. It's further divided into discrete and continuous data.
Accurate data classification ensures that the correct statistical techniques are applied. For example, knowing whether your data set involves discrete or continuous variables helps in selecting the right visualizations and statistical analyses, paving the way to more conclusive results.

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Most popular questions from this chapter

New Homes A contractor has four new home plans. Plan 1 is a home with six windows. Plan 2 is a home with seven windows. Plan 3 has eight windows, and plan 4 has nine windows. The probability distribution for the sale of the homes is shown. Find the mean, variance, and standard deviation for the number of windows in the homes that the contractor builds. $$ \begin{array}{c|cccc}{X} & {6} & {7} & {8} & {9} \\ \hline P(X) & {0.3} & {0.4} & {0.25} & {0.05}\end{array} $$

Use the multinomial formula and find the probabilities for each. $$ \begin{array}{l}{\text { a. } n=3, X_{1}=1, X_{2}=1, X_{3}=1, p_{1}=0.5, p_{2}=0.3} \\ {p_{3}=0.2} \\ {\text { b. } n=5, X_{1}=1, X_{2}=3, X_{3}=1, p_{1}=0.7, p_{2}=0.2} \\ {p_{3}=0.1} \\ {\text { c. } n=7, X_{1}=2, X_{2}=3, X_{3}=2, p_{1}=0.4, p_{2}=0.5} \\ {p_{3}=0.1}\end{array} $$

For Exercises 7 through 16, assume all variables are binomial. (Note: If values are not found in Table B of Appendix A, use the binomial formula.) Belief in UFOs A survey found that 10% of Americans believe that they have seen a UFO. For a sample of 10 people, find each probability: a. That at least 2 people believe that they have seen a UFO b. That 2 or 3 people believe that they have seen a UFO c. That exactly 1 person believes that he or she has seen a UFO

Survey of High School Seniors Of graduating high school seniors, 14% said that their generation will be remembered for their social concerns. If 7 graduating seniors are selected at random, find the probability that either 2 or 3 will agree with that statement.

2\. Which of the following are binomial experiments or can be reduced to binomial experiments? a. Testing one brand of aspirin by using 10 people to determine whether it is effective b. Asking 100 people if they smoke c. Checking 1000 applicants to see whether they were admitted to White Oak College d. Surveying 300 prisoners to see how many different crimes they were convicted of e. Surveying 300 prisoners to see whether this is their first offense
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