Basic Math

Data and graphs | Fourth Grade

Data and Graphs | Fourth Grade

Complete Notes & Formulas

1. Read a Table

Definition: A table organizes data in rows (horizontal) and columns (vertical) to make information easy to read and compare.

📊 Parts of a Table:

  • Title: Tells what the table is about
  • Column Headers: Labels at the top of columns
  • Row Headers: Labels on the left side
  • Data/Values: Numbers or information in cells

✏️ Example Table:

Favorite Fruits Survey

FruitNumber of Students
Apple15
Banana12
Orange8

Questions to ask: Which fruit is most popular? How many students chose banana?

💡 Reading Tips:

  • Read the title first to understand the data
  • Locate the row and column for the data you need
  • Follow the row across and column down to find the value
  • Check units (numbers, dollars, percentages, etc.)

2-3. Interpret and Create Bar Graphs

Definition: A bar graph uses rectangular bars to show and compare data. The length or height of each bar represents a value.

📐 Parts of a Bar Graph:

  • Title: Describes what the graph shows
  • Horizontal Axis (x-axis): Categories or labels
  • Vertical Axis (y-axis): Number scale
  • Bars: Show the value for each category
  • Scale: Numbers on the y-axis (intervals should be equal)

📝 Properties of Bar Graphs:

  • All bars have equal width
  • All bars have a common base
  • Height/length of bar = value of data
  • Equal spacing between bars

✏️ How to Create a Bar Graph:

  1. Step 1: Draw horizontal (x) and vertical (y) axes
  2. Step 2: Write title at the top
  3. Step 3: Label x-axis (categories) and y-axis (numbers)
  4. Step 4: Choose appropriate scale for y-axis
  5. Step 5: Draw bars with correct heights
  6. Step 6: Make sure bars are equal width with equal spacing

💡 Types of Bar Graphs:

  • Vertical Bar Graph: Bars go up from bottom to top
  • Horizontal Bar Graph: Bars go left to right

4-5. Interpret and Create Line Plots

Definition: A line plot (also called dot plot) shows data along a number line using X's or dots to represent frequency.

📊 Parts of a Line Plot:

  • Title: What the data represents
  • Number Line: Shows the range of values
  • X's or Dots: Each X represents one data point
  • Labels: Description of what is being measured

✏️ Example Line Plot:

Number of Pets Students Have

    X
    X           X
    X   X   X   X   X
    X   X   X   X   X   X
________________________________
0   1   2   3   4   5   6
        Number of Pets
                

Reading: 4 students have 0 pets, 3 students have 1 pet, etc.

📝 How to Create a Line Plot:

  1. Draw a horizontal number line
  2. Mark equal intervals based on data range
  3. Write a title above the plot
  4. Label the number line (what is being measured)
  5. Place an X above each number for each data point
  6. Stack X's if multiple data points have same value

💡 Uses of Line Plots:

  • Shows how data is distributed
  • Easy to see most common value (mode)
  • Can show data with fractions (like ½, ¼)
  • Good for small sets of numerical data

6. Frequency Tables

Definition: A frequency table shows how often each value or category appears in a data set. Frequency means "how many times."

📊 Parts of a Frequency Table:

  • Title: What data is being counted
  • Category Column: Lists items or values
  • Tally Column: Uses tally marks (||||) to count
  • Frequency Column: Shows total count as a number

✏️ Example Frequency Table:

Favorite Colors Survey

ColorTallyFrequency
Red|||| ||7
Blue|||| ||||10
Green||||5

📝 How to Create a Frequency Table:

  1. List all categories or values in first column
  2. Use tally marks to count (|||| = 5)
  3. Count tally marks and write frequency number
  4. Add all frequencies to find total

🔑 Key Formula:

Total = Sum of All Frequencies

7-8. Interpret and Create Stem-and-Leaf Plots

Definition: A stem-and-leaf plot organizes data by splitting each number into a "stem" (first digit(s)) and "leaf" (last digit).

📐 How Stem-and-Leaf Works:

For 2-digit numbers:

Stem = Tens digit

Leaf = Ones digit

Example: 47 → Stem = 4, Leaf = 7

For 3-digit numbers:

Stem = Tens and hundreds digits

Leaf = Ones digit

Example: 123 → Stem = 12, Leaf = 3

✏️ Example Stem-and-Leaf Plot:

Test Scores: 23, 27, 30, 35, 38, 42, 45, 49

StemLeaf
23 7
30 5 8
42 5 9

Key: 2|3 means 23

📝 How to Create Stem-and-Leaf Plot:

  1. Step 1: Arrange data in order (smallest to largest)
  2. Step 2: Draw a table with two columns: Stem | Leaf
  3. Step 3: Write all possible stem values in order
  4. Step 4: For each data point, write leaf digit next to stem
  5. Step 5: List leaves in order from smallest to largest
  6. Step 6: Include a key showing how to read the plot

💡 Advantages:

  • Shows all original data values
  • Easy to see distribution and gaps
  • Data is automatically organized
  • Can find mode, median, range easily

9. Choose the Best Type of Graph

Definition: Selecting the most appropriate graph type depends on the kind of data and what you want to show.

📊 Graph Selection Guide:

Use TABLE when:

  • You need exact values
  • Organizing lots of different information
  • Showing multiple categories with multiple values

Use BAR GRAPH when:

  • Comparing different categories or groups
  • Showing differences between groups clearly
  • Data is not continuous (separate categories)
  • Example: Favorite sports, types of animals

Use LINE PLOT when:

  • Showing frequency of numerical data
  • Data has specific values on a number line
  • Working with measurements or fractions
  • Example: Heights, shoe sizes, test scores

Use FREQUENCY TABLE when:

  • Counting how many times something occurs
  • Organizing data before making a graph
  • Recording survey results
  • Need to show tallies and totals

Use STEM-AND-LEAF PLOT when:

  • You want to see ALL individual data values
  • Data has 2 or 3 digits
  • Finding patterns in numerical data
  • Example: Ages, test scores, measurements

💡 Quick Decision Guide:

QuestionBest Graph Type
Compare categories?Bar Graph
Show frequency on number line?Line Plot
Keep all original values?Stem-and-Leaf Plot
Count occurrences?Frequency Table
Need exact values?Table

Data and Graphs Quick Reference Chart

Graph TypeBest Used ForKey Feature
TableOrganizing exact data in rows & columnsShows precise values
Bar GraphComparing categories or groupsUses rectangular bars
Line PlotShowing frequency of data valuesUses X's on number line
Frequency TableCounting how often data occursUses tally marks
Stem-and-Leaf PlotOrganizing numerical data by place valueSplits numbers: stem|leaf

📚 Fourth Grade Data and Graphs - Complete Study Guide

Master these data visualization skills for math excellence! ✨

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