Constructing the Frequency Histogram

Oct 13, 2025 by leolavanderia.com.br 140 views

Introduction

In mathematics, a frequency histogram is a graphical representation of data that displays the frequency or number of occurrences of different values in a dataset. It is a useful tool for understanding and visualizing the distribution of data, and is commonly used in statistics and data analysis. In this article, we will explore how to construct and label a frequency histogram of the data from a survey of 125 students at a local high school.

The Survey Data

A survey was given to 125 students at a local high school, asking how many minutes it takes them to commute to school. The results are summarized in the table below:

Commute Time (minutes)	Frequency
0-10	15
11-20	30
21-30	40
31-40	20
41-50	10
51-60	5
61-70	2
71-80	1
81-90	1
91-100	1

Constructing the Frequency Histogram

To construct a frequency histogram, we need to create a graph with the commute time on the x-axis and the frequency on the y-axis. The x-axis will be divided into intervals of 10 minutes, and the y-axis will be divided into intervals of 10.

Here is the frequency histogram:

Frequency Histogram

Labeling the Frequency Histogram

To label the frequency histogram, we need to add the following information:

Title: "Commute Time Frequency Histogram"
X-axis label: "Commute Time (minutes)"
Y-axis label: "Frequency"
Interval labels: "0-10", "11-20", "21-30", etc.
Tick marks: Add tick marks on the x-axis to indicate the intervals.

Here is the labeled frequency histogram:

Labeled Frequency Histogram

Discussion

The frequency histogram shows that the majority of students (40) take between 21-30 minutes to commute to school. This is followed by students who take between 11-20 minutes (30) and 0-10 minutes (15). The histogram also shows that there are fewer students who take longer than 30 minutes to commute to school.

Interpretation

The frequency histogram can be used to answer questions such as:

What is the most common commute time?
How many students take longer than 30 minutes to commute to school?
What is the distribution of commute times?

Conclusion

In conclusion, the frequency histogram is a useful tool for understanding and visualizing the distribution of data. By constructing and labeling a frequency histogram of the data from a survey of 125 students at a local high school, we can gain insights into the commute times of students and answer questions about the distribution of data.

Mathematical Concepts

The frequency histogram is based on the following mathematical concepts:

Frequency: The number of occurrences of a value in a dataset.
Histogram: A graphical representation of data that displays the frequency or number of occurrences of different values in a dataset.
Interval: A range of values that are grouped together in a histogram.

Real-World Applications

The frequency histogram has many real-world applications, including:

Statistics: Frequency histograms are used to understand and visualize the distribution of data in statistics.
Data analysis: Frequency histograms are used to analyze and understand the distribution of data in data analysis.
Business: Frequency histograms are used to understand and visualize the distribution of data in business, such as customer demographics and sales data.

Future Research

Future research could include:

Surveying a larger sample size: Surveying a larger sample size could provide more accurate and reliable results.
Using different types of data: Using different types of data, such as categorical or numerical data, could provide more insights into the distribution of data.
Analyzing the data using different statistical methods: Analyzing the data using different statistical methods, such as regression or time series analysis, could provide more insights into the distribution of data.
Frequently Asked Questions (FAQs) about Frequency Histograms ================================================================

Q: What is a frequency histogram?

A: A frequency histogram is a graphical representation of data that displays the frequency or number of occurrences of different values in a dataset.

Q: What is the purpose of a frequency histogram?

A: The purpose of a frequency histogram is to understand and visualize the distribution of data, and to answer questions about the data, such as what is the most common value, and how many values fall within a certain range.

Q: How is a frequency histogram constructed?

A: A frequency histogram is constructed by dividing the data into intervals, and then counting the number of values that fall within each interval. The intervals are then plotted on a graph, with the x-axis representing the interval and the y-axis representing the frequency.

Q: What are the benefits of using a frequency histogram?

A: The benefits of using a frequency histogram include:

Easy to understand: Frequency histograms are easy to understand, even for those without a strong mathematical background.
Visual representation: Frequency histograms provide a visual representation of the data, making it easier to identify patterns and trends.
Quick analysis: Frequency histograms can be used to quickly analyze large datasets, and to identify areas where further analysis is needed.

Q: What are some common mistakes to avoid when constructing a frequency histogram?

A: Some common mistakes to avoid when constructing a frequency histogram include:

Incorrect interval selection: Selecting intervals that are too large or too small can lead to inaccurate results.
Incorrect data preparation: Failing to prepare the data properly can lead to inaccurate results.
Incorrect graphing: Failing to graph the data correctly can lead to inaccurate results.

Q: How can I use a frequency histogram in real-world applications?

A: Frequency histograms can be used in a variety of real-world applications, including:

Business: Frequency histograms can be used to analyze customer demographics and sales data.
Statistics: Frequency histograms can be used to understand and visualize the distribution of data in statistics.
Data analysis: Frequency histograms can be used to analyze and understand the distribution of data in data analysis.

Q: What are some common types of data that can be analyzed using a frequency histogram?

A: Some common types of data that can be analyzed using a frequency histogram include:

Categorical data: Frequency histograms can be used to analyze categorical data, such as customer demographics.
Numerical data: Frequency histograms can be used to analyze numerical data, such as sales data.
Time series data: Frequency histograms can be used to analyze time series data, such as stock prices.

Q: How can I create a frequency histogram using software?

A: Frequency histograms can be created using a variety of software, including:

Microsoft Excel: Frequency histograms can be created using Microsoft Excel's charting tools.
Google Sheets: Frequency histograms can be created using Google Sheets' charting tools.
R: Frequency histograms can be created using R's ggplot2 package.

Q: What are some common challenges when working with frequency histograms?

A: Some common challenges when working with frequency histograms include:

Data preparation: Failing to prepare the data properly can lead to inaccurate results.
Interval selection: Selecting intervals that are too large or too small can lead to inaccurate results.
Graphing: Failing to graph the data correctly can lead to inaccurate results.

Q: How can I troubleshoot common issues with frequency histograms?

A: Some common issues with frequency histograms can be troubleshooted by:

Checking data preparation: Ensuring that the data is properly prepared can help to identify and resolve issues.
Checking interval selection: Ensuring that the intervals are correctly selected can help to identify and resolve issues.
Checking graphing: Ensuring that the data is correctly graphed can help to identify and resolve issues.