Histogram

A histogram is a graphical representation of the distribution of numerical data. It is a type of bar graph that displays the frequency or proportion of data within certain intervals or ranges. Histograms are used to visualize the shape, center, and spread of the data, and to identify any patterns or outliers.

Components of a Histogram

There are several key components of a histogram:

Bars: The bars in a histogram represent the intervals or ranges of the data, and their heights correspond to the frequency or proportion of data within each interval.
Intervals or Bins: These are the ranges of values that the data is divided into for the purpose of creating the histogram. The intervals should be of equal width and non-overlapping.
Frequency: The frequency of a particular interval is the number of data points that fall within that interval.
Title and Axes: A histogram should have a descriptive title, as well as labeled x and y axes that indicate the variable being measured and the frequency or proportion, respectively.
Relative Frequency: In addition to the frequency, the proportion of data points within each interval can be used to create a relative frequency histogram.

Creating a Histogram

To create a histogram, follow these steps:

Choose the appropriate number of intervals or bins for the data.
Determine the range of the data and calculate the width of each interval.
Create a frequency table that lists the intervals and the frequency of data points within each interval.
Draw the x and y axes, and label them appropriately.
For each interval, draw a bar whose height corresponds to the frequency or proportion of data within that interval.
Add a title and a key if necessary.

Interpreting a Histogram

When interpreting a histogram, consider the following:

Shape: Is the distribution symmetric, skewed to the left or right, unimodal, bimodal, or multimodal?
Center: Where is the center of the distribution located?
Spread: What is the range of the data and how spread out are the values?
Outliers: Are there any data points that fall far from the main concentration of the data?
Trends and Patterns: Are there any noticeable trends or patterns in the data?

Study Guide

To study histograms, it's important to understand the following concepts:

How to create a frequency table from given data.
How to determine the appropriate number of intervals or bins for a given set of data.
How to calculate the width of each interval.
How to interpret the shape, center, and spread of a distribution based on a histogram.
How to identify and analyze outliers in a histogram.

Additionally, practicing with sample problems and real-world data sets can help reinforce your understanding of histograms and their interpretation.

By mastering the concepts and techniques related to histograms, you'll be well-equipped to analyze and interpret various types of data distributions in the future.

◂Math Worksheets and Study Guides Eighth Grade. Real numbers

The resources above cover the following skills:

The Number System

Know that there are numbers that are not rational, and approximate them by rational numbers.

Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number. [8-NS1]

Expressions and Equations

Work with radicals and integer exponents.

Use square root and cube root symbols to represent solutions to equations of the form x^2 = p and x^3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational. [8-EE2]