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E12 • Lesson 12 of 105

Data & Basic Graphing

Collecting data, pictographs, bar graphs, interpretation

Elementary Foundations • K-5

Key Concepts

  • data
  • graphing
  • representation

Data and Basic Graphing

Data is information we collect about the world. How many students walk to school? What is the most popular ice cream flavor? When we organize data into graphs, it becomes easy to see patterns, compare groups, and answer questions. Let's learn how to collect, organize, and display data!

Collecting and Organizing Data

The first step is to collect data by counting, measuring, or surveying. Then organize it in a tally chart or frequency table.

Making a Tally Chart

A class voted for their favorite fruit. Here are the results:

FruitTalliesCount
Apple|||| ||7
Banana||||5
Grape|||| |||8
Orange||||4

Every fifth tally mark crosses the previous four (||||), making groups of five that are easy to count.

Pictographs

A pictograph uses pictures or symbols to show data. Each picture stands for a certain number of items.

Reading a Pictograph

Books read by each student (each symbol = 2 books):

Ana    : ★ ★ ★ ★

Ben    : ★ ★ ★

Cara   : ★ ★ ★ ★ ★

Key: ★ = 2 books

Ana: 4 stars x 2 = 8 books
Ben: 3 stars x 2 = 6 books
Cara: 5 stars x 2 = 10 books

Bar Graphs

A bar graph uses bars of different lengths to show data. The taller the bar, the greater the value.

Every bar graph needs:

Reading a Bar Graph

Using the fruit data from above, imagine bars going up from each fruit name:

8 |                ██

7 |  ██

6 |  ██

5 |  ██  ██  ██

4 |  ██  ██  ██  ██

3 |  ██  ██  ██  ██

2 |  ██  ██  ██  ██

1 |  ██  ██  ██  ██

  +--Apple-Banana-Grape-Orange

Questions you can answer from this graph:

  • Which fruit is most popular? Grape (tallest bar = 8)
  • Which is least popular? Orange (shortest bar = 4)
  • How many more votes did Apple get than Orange? 7 - 4 = 3 more
  • How many votes in all? 7 + 5 + 8 + 4 = 24 total

Interpreting Data

Once data is displayed, you can answer important questions:

Common Mistake

In pictographs, students forget to use the key. If each picture equals 2 items and you see 5 pictures, the answer is NOT 5 -- it is 5 x 2 = 10. Always check the key before reading the data!

Helpful Tip

When making your own bar graph, choose a scale that fits your data. If your biggest value is 20, count by 2s or 5s. If it is 100, count by 10s or 20s. The scale should make the graph easy to read without being too tall or too squished.

Practice Problems

1. In a pictograph, each star symbol equals 3 votes. If the "Pizza" row shows 6 stars, how many votes did Pizza get?

Show Solution

6 stars x 3 votes each = 18 votes.

2. Look at this data: Red = 12, Blue = 8, Green = 15, Yellow = 5. Which color is most popular? Which is least?

Show Solution

Most popular: Green (15). Least popular: Yellow (5).

3. Using the data from problem 2, how many more people chose Green than Blue?

Show Solution

15 - 8 = 7 more people chose Green than Blue.

4. A bar graph shows: Monday = 3 books, Tuesday = 5, Wednesday = 2, Thursday = 6, Friday = 4. How many total books were read?

Show Solution

3 + 5 + 2 + 6 + 4 = 20 books total.

5. You surveyed 5 friends about their favorite pet. Results: Dog = 8, Cat = 6, Fish = 3, Bird = 3. If you made a pictograph where each symbol equals 2, how many symbols would you draw for Cat?

Show Solution

6 ÷ 2 = 3 symbols for Cat.

Summary: Data is information we collect and organize. Tally charts, pictographs, and bar graphs are three ways to display data visually. Every pictograph needs a key, and every bar graph needs a title, labels, and a scale. Once data is graphed, you can answer comparison and total questions easily.

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