Math 06 Unit 10 Understanding Data Representation Techniques

What is a box plot used to represent?

• The average of a set of data

• The five-number summary of data

• The frequency of data in certain ranges

• The most frequent piece of data

Answer explanation

A box plot visually represents the five-number summary of data: minimum, first quartile, median, third quartile, and maximum. It does not show averages, frequencies, or modes.

Which of the following is an example of categorical data?

• The height of students in a class

• The number of books in a library

• The favorite color of students in a class

• The temperature in a city

Answer explanation

Categorical data represents categories or groups. 'The favorite color of students in a class' is categorical as it describes preferences, while the other options are numerical or continuous data.

What does a dot plot use to show the frequency of data?

• Bars

• Lines

• Dots or Xs

• Circles

Answer explanation

A dot plot uses dots or Xs to represent the frequency of data points. Each dot or X corresponds to a count, making it easy to visualize the distribution of values in a dataset.

What is the interquartile range (IQR)?

• The difference between the maximum and minimum values

• The average of a set of data

• The difference between the first quartile and the third quartile

• The most frequent value in a set of data

How is the mean of a set of data calculated?

• By finding the middle number of the data set

• By finding the most frequent number in the data set

• By adding all the numbers and dividing by the number of pieces of data

• By subtracting the smallest number from the largest number

Answer explanation

The mean is calculated by adding all the numbers in the data set and then dividing by the total number of values. This method provides the average value, making it the correct choice among the options.

What is the mode of a set of data?

• The average of the data

• The middle number of the data

• The most frequent piece of data

• The range of the data

Answer explanation

The mode of a set of data is defined as the most frequent piece of data. It represents the value that appears most often in the dataset, distinguishing it from the average and median.

Which of the following is an example of numerical data?

• Types of fruits

• The number of students in a class

• Colors of cars

• Brands of shoes

Answer explanation

Numerical data refers to information that can be quantified. 'The number of students in a class' is numerical because it represents a count, while the other options describe categories or types, not quantities.

What does a histogram represent?

• The five-number summary of data

• The frequency of data in certain ranges

• The most frequent category in a set of data

• The average of a set of data

Answer explanation

A histogram visually represents the frequency of data within specified ranges, allowing us to see how data is distributed across different intervals. This makes 'the frequency of data in certain ranges' the correct choice.

What is the range of a set of data?

• The difference between the first quartile and the third quartile

• The average of the data

• The difference between the greatest and least number

• The most frequent value in the data

Answer explanation

The range of a set of data is defined as the difference between the greatest and least number in that set. This choice accurately describes how to calculate the range, making it the correct answer.

What is a stem-and-leaf plot used for?

• To show the average of a set of data

• To analyze and compare groups of numerical data

• To represent the frequency of data in certain ranges

• To show the five-number summary of data

Answer explanation

A stem-and-leaf plot is specifically designed to analyze and compare groups of numerical data by displaying the distribution while retaining the original data values, making it easier to identify patterns and differences.