Mathematics
Grade 9
15 min
Create bar graphs
Create bar graphs
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1
Introduction & Learning Objectives
Learning Objectives
Identify the essential components of a bar graph, including title, axes, labels, and scale.
Differentiate between categorical and numerical data to determine when a bar graph is the appropriate visualization tool.
Calculate and select an appropriate and consistent scale for the frequency axis based on a given data set.
Construct an accurate, well-labeled single bar graph from a frequency table.
Create a clustered (or double) bar graph to compare two related data sets.
Interpret the information presented in a bar graph to draw valid conclusions and make comparisons between categories.
Critically evaluate a bar graph for potentially misleading features, such as an inconsistent or truncated scale.
Ever wonder how companies like Spotify or YouTube know exac...
2
Key Concepts & Vocabulary
TermDefinitionExample
Categorical DataData that can be sorted into distinct, non-numerical groups or categories. Bar graphs are specifically designed to display this type of data.Favorite movie genres (Comedy, Action, Sci-Fi), car brands (Ford, Toyota, Honda), or eye color (Blue, Brown, Green).
FrequencyThe number of times a specific category or value appears in a data set.In a survey of 30 students, if 12 chose 'Pizza' as their favorite food, the frequency for the 'Pizza' category is 12.
AxesThe two perpendicular lines that form the framework of a graph. The horizontal line is the x-axis (usually for categories), and the vertical line is the y-axis (usually for frequency).On a graph of favorite pets, the x-axis would list 'Dogs', 'Cats', 'Fish...
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Core Formulas
Scale Interval Selection
Scale\,Increment \approx \frac{Maximum\,Data\,Value}{Desired\,Number\,of\,Intervals}
To create a clean and readable y-axis, divide your highest data value by the number of gridlines you want (usually 5 to 10). Then, round your result UP to a 'friendly' number like 1, 2, 5, 10, 20, 50, or 100. This ensures the scale is consistent and easy to interpret.
Relative Frequency Calculation
f_{rel} = \frac{f_i}{\sum f} \times 100\%
To express the frequency of a category as a percentage of the total, divide the frequency of that single category (f_i) by the sum of all frequencies (Σf, the total number of data points). This is useful for creating a relative frequency bar graph, where the y-axis shows percentages instead of counts.
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Challenging
In the 'Console Preferences' example, a game developer claims, 'Among Grade 10s, Xbox is more than twice as popular as Nintendo.' They present a bar graph where the y-axis starts at 20 to support this. Why is this graph visually misleading, even if the raw numbers (Xbox: 55, Nintendo: 25) are accurate?
A.The graph should have been a pie chart instead.
B.The title of the graph is likely incorrect.
C.The legend is missing, so the bars are unidentifiable.
D.The truncated y-axis makes the Xbox bar appear proportionally much larger than it truly is compared to the Nintendo bar.
Challenging
A survey of 60 students on their favorite social media platform yields: TikTok (28), Instagram (19), Snapchat (13). You create a bar graph with a y-axis from 0 to 30 with increments of 5. Now, 12 more students are surveyed, and all of them choose TikTok. How must you adjust the y-axis to best accommodate the new data?
A.Keep the scale the same, as the new maximum is only 40.
B.Change the scale to start at 10 to save space.
C.Change the maximum to 45 or 50 and keep the increment at 5.
D.Change the increment to 20 to make the graph smaller.
Challenging
A clustered bar graph compares two data series, 'Series 1' (blue bars) and 'Series 2' (red bars), across four groups (A, B, C, D). The legend is missing. You are told two facts: 1) For every group, the value of Series 1 is greater than the value of Series 2. 2) The total value (Series 1 + Series 2) for Group C is the highest among all groups. Based on the visual representation, what can you definitively conclude?
A.The blue bars are taller than the red bars within each cluster.
B.The red bars in cluster C are the tallest red bars on the entire graph.
C.The blue bar in cluster C is the tallest bar on the entire graph.
D.The sum of the heights of the bars in cluster A is the lowest.
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