Investigation 5: Creating Graphs

New Concept

This course builds your mathematical foundation. You will learn to use numbers, operations, and data displays to understand patterns and solve real-world problems.

What’s next

To begin, we will explore a key tool for data analysis. Next, you’ll get a visual breakdown of how to create and interpret different graphs.

Property

A histogram is a special type of bar graph that displays data in equal-sized intervals. There are no spaces between the bars.

Examples

• Test scores from 80-100 are grouped: 80-84 (5 students), 85-89 (12 students), 90-94 (8 students), 95-100 (3 students). The tallest bar is for the 85-89 interval.
• A histogram shows the ages of visitors at a park: 15 people are aged 0-9, 25 are 10-19, 30 are 20-29, and 10 are 30-39.
• A histogram displays monthly rainfall. January: 0-2 inches, February: 0-2 inches, March: 2-4 inches, April: 4-6 inches. The bars show a trend of increasing rainfall.

Explanation

Think of a histogram as a city skyline where each building represents a group of data, like test scores. The buildings have no gaps because the data intervals are continuous. The taller the building, the more data points, or 'people,' are inside that score range. It's a quick way to see where most of the action is happening!

Property

A double-line graph may compare two performances over time.

Examples

• Comparing two companies' stock values: Year 1 (A: 20 dollars, B: 25 dollars), Year 2 (A: 22 dollars, B: 28 dollars), Year 3 (A: 30 dollars, B: 29 dollars).
• Tracking weekly reading for two students, Maria and Sam. Week 1 (Maria: 30 pages, Sam: 45 pages), Week 2 (Maria: 40 pages, Sam: 40 pages), Week 3 (Maria: 50 pages, Sam: 35 pages).
• A graph shows the population growth of two towns, Springfield and Shelbyville, over 10 years. Springfield's line starts lower but has a steeper slope.

Explanation

Imagine you are tracking the growth of two different tomato plants over a month. A double-line graph lets you plot both plants' heights on the same chart, using different colored lines. This makes it super easy to see which plant grew faster, when they were the same height, or how the gap between them changed over time.

Property

A circle graph (or pie graph) is commonly used to show components of a budget. To make a sector, calculate its percentage of $360^{\circ}$.

Examples

• A survey of favorite pets: 50% Dogs, 25% Cats, 15% Fish, 10% Other. The 'Dogs' sector would be a $180^{\circ}$ angle, taking up half the circle.
• A student's daily schedule: Sleep (40%), School (25%), Homework (10%), Other (25%). The angle for Sleep is $0.40 \times 360^{\circ} = 144^{\circ}$.
• A class fundraiser of 500 dollars. Bake sale: 250 dollars (50%), Car wash: 150 dollars (30%), Donations: 100 dollars (20%).

Explanation

A circle graph is like slicing up a pizza, where each slice represents a category. The whole pizza is 100 percent of your data, like your monthly allowance. Bigger slices mean bigger percentages! It’s perfect for showing how a whole is divided, like how you spend your time in a day or what types of music your friends prefer.