Bar Graphs Explained

Bar Graphs

• A bar graph is a graph with bars representing the frequency or relative frequency of a particular category.
• Used to organize qualitative data.
• Bars do not touch one another.
• Can be presented vertically or horizontally.
• The height of each bar indicates the frequency or relative frequency of that category.

Frequencies vs. Relative Frequencies

• Frequencies: Actual counts of items in each category (e.g., number of cats).
• Relative Frequencies: Percentages or proportions of items in each category.
• When looking at a bar chart, determine whether frequencies or relative frequencies are being used.

Example: Favorite Animals

• Miss Ellison asked her second-grade students to identify their favorite animal.
• Categories:
  • Dog
  • Cat
  • Bird
  • Dinosaur
  • Horse
  • Other

Reading the Bar Chart

• The height of the bar represents the number of students who chose that animal.
  • Dog: 8 students
  • Cat: 7 students
  • Bird: 2 students
  • Dinosaur: 6 students
  • Horse: 4 students
  • Other: 3 students

Calculating Totals and Percentages

• Total Students: Sum of frequencies for each category.
  • $8 + 7 + 2 + 6 + 4 + 3 = 30$
  • There are 30 students represented in the bar chart.

Combining Categories

• How many students chose dogs or cats?
  • $8 \, (dogs) + 7 \, (cats) = 15 \, students$

Relative Frequency Calculation

• Percentage of students who chose dogs or cats:
  • $\frac{15}{30} \times 100 = 50 \%$
  • 15 students chose dogs or cats out of 30 total students.
  • 50% of the students chose dogs or cats as their favorite animal.

When Given Frequencies

• We can add counts to find totals.
• We can calculate percentages (relative frequencies) by dividing the category frequency by the total and multiplying by 100.

Relative Frequency Formula

• $\text{Relative Frequency} = \frac{\text{Category Frequency}}{\text{Total}} \times 100 \%$

Bar Charts with Relative Frequencies

• If the bar chart provides relative frequencies (percentages) instead of frequencies (counts), we need the total number of items to determine the actual number of items in each category, similar to pie charts.