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Chapter 2: Problem 22

The cumulative relative frequency for the last class must always be 1. Why?

Short Answer

Expert verified
The cumulative relative frequency for the last class must be 1 because it includes the entire dataset.

Step by step solution

01

Understanding Cumulative Relative Frequency

Cumulative Relative Frequency is the accumulation of the previous relative frequencies. It is calculated by adding each relative frequency from the frequency distribution table to the total of the relative frequencies preceding the class being considered.
02

Formulating Total Relative Frequency

Remember that the relative frequency of each class is the frequency of that class divided by the total number of data points. Thus, the sum of all the relative frequencies will equal 1 because it represents the whole dataset.
03

Cumulative Relative Frequency of Last Class

As you progress from the first class to the last, you keep adding relative frequencies. By the time you have added the relative frequency of the last class, you will have included all data points in the dataset. Therefore, the cumulative relative frequency for the last class should always sum up to 1, representing 100% of the data.

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Key Concepts

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

Relative Frequency
Relative frequency is a way of expressing how often something happens relative to the total number of observations. Instead of just counting occurrences, relative frequency gives us the proportion. For example, if you have a dataset with 20 total observations and a specific event happens 5 times, the relative frequency of that event is \(\frac{5}{20} = 0.25\) or 25%.
To calculate the relative frequency, simply divide the frequency of a specific event by the total number of observations in the dataset. This is particularly useful in comparing different datasets or events because it standardizes the results.
Frequency Distribution Table
A frequency distribution table is a way to organize data into categories or classes. Each category shows the number of observations falling into each range or class.
For instance, if you have exam scores ranging from 0 to 100, you can create a frequency distribution table where each class represents a score range like 0-10, 11-20, and so on. The table will have:
  • Classes (score ranges)
  • Frequencies (counts of observations within each class)
  • Relative Frequencies (frequencies divided by the total number of observations)
This table helps visualize data, making it easier to understand distributions and identify trends or patterns quickly.
Dataset
A dataset is a collection of data points or values. It can include anything from numbers and measurements to categories and text entries. There are different kinds of datasets, including:
  • Quantitative (numerical) datasets, like test scores or temperatures
  • Qualitative (categorical) datasets, like types of fruits or genres of books
To work with a dataset, you often need to organize it into a format that makes analysis easier, such as a frequency distribution table. By organizing data, you can perform calculations like finding the mean, median, and standard deviation, or creating graphs and charts to illustrate relationships and trends.

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Most popular questions from this chapter

Determine the original set of data. $$ \begin{aligned} &\begin{array}{l|l} 12 & 3799 \\ 13 & 0457899 \\ 14 & 2447789 \\ 15 & 12256 \\ 16 & 03 \end{array}\\\ &\text { Legend: } 12 \mid 3 \text { represents } 12.3 \end{aligned} $$

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