Data and Graphs - Fifth Grade

Complete Notes & Formulas

Understanding Data

What is Data?

Data is a collection of facts, numbers, or measurements that we gather to learn something or answer questions.

Key Terms

Data: Information collected through observations or measurements

Frequency: How many times a value appears in a data set

Graph: A visual way to display data

Scale: The numbers on the axes that show the size of data

Trend: A pattern or direction that data follows

1. Line Plots (Dot Plots)

What is a Line Plot?

A line plot (also called a dot plot) shows frequency of data along a number line. Each data value is represented by an X or dot above the number line.

Parts of a Line Plot

1. Title: Describes what the data represents

2. Number Line: Shows the scale (with whole numbers, fractions, or decimals)

3. Marks (X or dots): Each mark represents one data point

4. Label: Tells what unit is being measured

Creating Line Plots

A. Line Plots with Whole Numbers

Steps:

1. Draw a number line with appropriate scale

2. Mark each data value with an X above the line

3. Stack X's if a value appears multiple times

4. Add title and labels

Example: Ages of students: 10, 11, 10, 12, 11, 10, 11, 12

Student Ages

X
X X
X X X
--|--|--|
10 11 12

3 students are 10 years old

B. Line Plots with Decimals

Example: Plant heights in meters: 0.5, 0.75, 1.0, 0.5, 0.75, 1.25

• Scale uses decimal increments (0.25, 0.5, 0.75, 1.0, 1.25)

• Each X represents one measurement

Two plants are 0.5 m tall

C. Line Plots with Fractions

Common Fractions: 1/8, 1/4, 1/2, 3/4, etc.

Example: Ribbon lengths in feet: 1/4, 1/2, 3/4, 1/2, 1/4, 1/2, 1

• Number line shows: 0, 1/4, 1/2, 3/4, 1

• Stack X's above each fraction

Three ribbons are 1/2 foot long

Interpreting Line Plots

Questions to Ask:

• What is the most common value? (Mode)

• What is the range? (Largest − Smallest)

• How many total data points?

• What is the total sum? (For fractions: add all values)

Multi-Step Problems with Line Plots

"A line plot shows pencil lengths: 1/4 ft (2 times), 1/2 ft (3 times), 3/4 ft (2 times). What is the total length of all pencils?"

Step 1: Multiply each value by its frequency

• 1/4 × 2 = 2/4 = 1/2 ft

• 1/2 × 3 = 3/2 = 1 1/2 ft

• 3/4 × 2 = 6/4 = 1 1/2 ft

Step 2: Add all amounts

1/2 + 1 1/2 + 1 1/2 = 3 1/2 ft

Answer: 3 1/2 feet total

2. Line Graphs

What is a Line Graph?

A line graph uses points connected by lines to show how data changes over time or across categories.

Parts of a Line Graph

Part	Description
Title	Tells what the graph shows
X-axis (horizontal)	Usually shows time or categories
Y-axis (vertical)	Shows the measured values
Scale	Numbers on each axis
Points	Mark the data values
Lines	Connect the points to show trends

Creating a Line Graph

Step 1: Draw and label the axes

Step 2: Choose an appropriate scale

Step 3: Plot each data point

Step 4: Connect points with straight lines

Step 5: Add a title

Interpreting Line Graphs

Look for:

• Increasing trend: Line goes up (data increases)

• Decreasing trend: Line goes down (data decreases)

• Constant: Line is flat (data stays the same)

• Highest/Lowest points: Maximum and minimum values

Example

Temperature by Hour:

Time	8 AM	10 AM	12 PM	2 PM
Temp (°F)	65	70	75	72

Temperature increased until 12 PM, then decreased!

3. Bar Graphs

What is a Bar Graph?

A bar graph uses rectangular bars to compare quantities. The length or height of each bar represents the value.

Types of Bar Graphs

Vertical Bar Graph: Bars go up and down

• Categories on x-axis (horizontal)

• Values on y-axis (vertical)

Horizontal Bar Graph: Bars go left and right

• Categories on y-axis (vertical)

• Values on x-axis (horizontal)

Creating a Bar Graph

Step 1: Draw and label axes

Step 2: Choose a scale (must fit all data)

Step 3: Draw bars for each category

Step 4: Make bars the same width

Step 5: Leave space between bars

Step 6: Add title

Interpreting Bar Graphs

Compare bar heights to compare values

Tallest bar = Greatest value

Shortest bar = Smallest value

Multi-Step Problems

"A bar graph shows: Apples=20, Oranges=35, Bananas=25. How many more oranges than apples were sold?"

Step 1: Find values: Oranges = 35, Apples = 20

Step 2: Subtract: 35 − 20 = 15

Answer: 15 more oranges

4. Frequency Tables

What is a Frequency Table?

A frequency table organizes data by showing how often each value appears.

Parts of a Frequency Table

Column	What it Shows
Category/Value	The items or values being counted
Tally	Marks to count (\|\|\|\| = 5)
Frequency	The number count for each category
Total	Sum of all frequencies

Creating a Frequency Table

Step 1: List all different values/categories

Step 2: Count how often each appears (use tallies)

Step 3: Write the frequency number

Step 4: Find the total

Example

Favorite Colors: Red, Blue, Red, Green, Blue, Blue, Red, Green, Blue

Color	Tally	Frequency
Red	\|\|\|	3
Blue	\|\|\|\|	4
Green	\|\|	2
Total	—	9

Blue is the most popular color!

Multi-Step Problems

Tip: Use frequency tables to find totals, differences, and patterns in data!

5. Stem-and-Leaf Plots

What is a Stem-and-Leaf Plot?

A stem-and-leaf plot organizes numerical data by splitting each number into a stem (leading digit(s)) and leaf (last digit).

How It Works

Stem: The tens digit (or higher place values)

Leaf: The ones digit

Example: For 35, stem = 3, leaf = 5

Creating a Stem-and-Leaf Plot

Step 1: Order data from smallest to largest

Step 2: Separate stem and leaf for each number

Step 3: List stems in order (vertically)

Step 4: Write leaves next to their stems (in order)

Step 5: Include a key to explain the plot

Example

Test Scores: 72, 85, 78, 92, 88, 75, 93, 81, 87

Ordered: 72, 75, 78, 81, 85, 87, 88, 92, 93

Stem	Leaf
7	2 5 8
8	1 5 7 8
9	2 3

Key: 7 | 2 represents 72

Most scores are in the 80s!

Interpreting Stem-and-Leaf Plots

• Easy to see the shape of data

• Shows the range (highest − lowest)

• Can identify clusters (where data groups)

• Keeps original data values

6. Scatter Plots

What is a Scatter Plot?

A scatter plot shows the relationship between two sets of data using points on a coordinate plane.

Parts of a Scatter Plot

X-axis: One variable (independent)

Y-axis: Another variable (dependent)

Points: Each represents a pair of data values

Pattern: Shows if variables are related

Creating a Scatter Plot

Step 1: Draw axes and label them

Step 2: Choose appropriate scales

Step 3: Plot each pair of values as a point

Step 4: Do NOT connect the points

Step 5: Add title

Types of Relationships

Relationship	Pattern	Example
Positive Correlation	Points go up and to the right	Study time vs. test scores
Negative Correlation	Points go down and to the right	TV time vs. homework done
No Correlation	Points scattered randomly	Shoe size vs. favorite color

Predictions and Trends

Trend Line = A line that follows the pattern of points

Use the trend to make predictions!

Example

Hours of Practice vs. Free Throws Made:

Hours	1	2	3	4
Free Throws	3	5	7	9

Positive correlation: More practice → More free throws made!

Prediction: After 5 hours, expect about 11 free throws

Quick Reference: Choosing the Right Graph

Graph Type	Best Used For
Line Plot	Showing frequency of data values
Line Graph	Showing change over time
Bar Graph	Comparing different categories
Frequency Table	Organizing and counting data
Stem-and-Leaf Plot	Showing data distribution (keeps actual values)
Scatter Plot	Showing relationships between two variables