MathIsimple

Lesson 6-1: Complex Charts & Graphs

Master the art of reading and creating double bar charts and pie charts with real-world data analysis.

Data Analysis
Charts & Graphs
Statistics
Visualization
What You'll Learn
  • • Read and interpret double bar charts comparing two data sets
  • • Understand pie charts and calculate percentages from sectors
  • • Create accurate charts from given data
  • • Compare data across different categories and time periods
  • • Draw conclusions and make predictions from charts
Double Bar Charts

What is a Double Bar Chart?

A double bar chart shows two sets of data side by side, making it easy to compare different categories or groups. Each category has two bars - one for each data set.

Example: Sports Team Performance

Let's compare the wins and losses for two basketball teams over 4 months:

Team A: Jan (8 wins, 2 losses), Feb (6 wins, 4 losses), Mar (10 wins, 0 losses), Apr (7 wins, 3 losses)

Team B: Jan (5 wins, 5 losses), Feb (7 wins, 3 losses), Mar (6 wins, 4 losses), Apr (9 wins, 1 loss)

How to Read a Double Bar Chart:

  1. Look at the title and labels to understand what's being compared
  2. Check the scale on the y-axis to understand the values
  3. Compare the heights of bars within each category
  4. Look for patterns across different categories
  5. Calculate differences between the two data sets

Practice Problem

Question: In which month did Team A have the best performance? How many more wins than losses did they have that month?

Your answer:

Pie Charts

Understanding Pie Charts

A pie chart shows parts of a whole as slices of a circle. Each slice represents a portion of the total, and all slices together make up 100%.

Example: Favorite Ice Cream Flavors

A survey of 120 students showed their favorite ice cream flavors:

• Chocolate: 48 students (40%)

• Vanilla: 36 students (30%)

• Strawberry: 24 students (20%)

• Mint: 12 students (10%)

How to Read a Pie Chart:

  1. Look at the title to understand what the chart represents
  2. Check the legend to identify what each color represents
  3. Compare slice sizes to see which categories are largest/smallest
  4. Use percentages to understand exact proportions
  5. Calculate actual numbers when given percentages

Calculating from Pie Charts

Formula: Number of items = (Percentage ÷ 100) × Total

Example: If 25% of 200 students prefer pizza, how many students is that?

Solution: (25 ÷ 100) × 200 = 0.25 × 200 = 50 students

Creating Your Own Charts

Steps to Create a Double Bar Chart

  1. Choose appropriate scales for both axes
  2. Label the x-axis with categories
  3. Label the y-axis with values
  4. Draw bars for the first data set
  5. Draw bars for the second data set next to the first
  6. Use different colors or patterns to distinguish the data sets
  7. Add a title and legend

Steps to Create a Pie Chart

  1. Calculate the percentage for each category
  2. Convert percentages to degrees (multiply by 3.6)
  3. Use a protractor to draw each slice
  4. Label each slice with the category name and percentage
  5. Use different colors for each slice
  6. Add a title and legend

Practice Activity

Create a pie chart showing how you spend your day (24 hours):

• Sleep: 8 hours

• School: 7 hours

• Homework: 2 hours

• Play/Free time: 4 hours

• Meals: 2 hours

• Other activities: 1 hour

Real-World Applications

Double Bar Charts Are Used For:

  • • Comparing sales between two stores
  • • Showing temperature differences between cities
  • • Comparing test scores before and after study
  • • Analyzing population growth in different regions
  • • Comparing expenses vs. income over time

Pie Charts Are Used For:

  • • Showing budget allocation
  • • Displaying survey results
  • • Representing market share
  • • Showing time distribution
  • • Displaying demographic data
Practice Problems

Problem 1: Double Bar Chart Analysis

A double bar chart shows the number of books read by students in two classes over 4 months. Class A read: Jan(12), Feb(15), Mar(18), Apr(20). Class B read: Jan(10), Feb(14), Mar(16), Apr(22).

Questions:

  1. Which class read more books in total?
  2. In which month was the difference between classes the greatest?
  3. How many more books did Class A read than Class B in March?

Problem 2: Pie Chart Calculations

A pie chart shows the distribution of 300 votes in a school election: Sarah (45%), Mike (30%), Lisa (15%), and Tom (10%).

Questions:

  1. How many votes did Sarah receive?
  2. How many more votes did Mike get than Lisa?
  3. What percentage of votes did Sarah and Mike receive together?

Problem 3: Chart Creation

Create a double bar chart showing the favorite sports of boys and girls in your class:

Boys: Soccer (8), Basketball (6), Swimming (4), Tennis (2)

Girls: Soccer (6), Basketball (8), Swimming (5), Tennis (3)

Then answer: Which sport is most popular overall?

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