Build a bar chart from a frequency table

Netball

\(\displaystyle 9\)

Football

\(\displaystyle 6\)

Basketball

\(\displaystyle 5\)

Tennis

\(\displaystyle 5\)

Students surveyed

\(\displaystyle 25\)

Axis unit

\(\displaystyle \%\)

25 students named their favourite sport. The results are to be drawn on a bar chart whose vertical axis shows percentage frequency. What height should the netball bar reach?

Keep the cycling count at 8 but increase the total sample from 20 to 80. Predict what happens to the cycling percentage

Keep the cycling count at 8 and move the total from 20 to 80. Both bars use the same percentage axis. Then keep the total fixed and vary the cycling count

With the count fixed at 8, what happened as the total grew?

Building a bar chart

Each bar shows its own category's value on the scale named on the vertical axis. A frequency bar shows the count, while a percentage bar shows the count as a share of the total

1. 1Match the vertical scale Read the vertical axis first. A percentage axis needs each count divided by the total and multiplied by 100. \(\displaystyle \frac{9}{25}=36\%\)
2. 2Keep categories separate Use one bar for each category and leave gaps between the bars
3. 3Use each category's height The height of a bar is the value for its own category, not the largest value \(\displaystyle \text{bar heights: }4,7,2\)
4. 4Choose a useful maximum Start at zero and use equal tick steps. For a tallest bar of 8, ticks from 0 to 10 in steps of 2 give one step of headroom \(\displaystyle 0,2,4,6,8,10\)

Group A

\(\displaystyle 20/100\)

Group B

\(\displaystyle 12/40\)

Group A has 20 cyclists out of 100 people. Group B has 12 cyclists out of 40. Which group has the larger cycling percentage?

Walk count

\(\displaystyle 14\)

Bus count

\(\displaystyle 10\)

Car count

\(\displaystyle 6\)

Cycle count

\(\displaystyle 10\)

Students in the class

\(\displaystyle 40\)

40 students in one class were asked how they get to school. The results are to be drawn on a bar chart whose vertical axis shows percentage frequency. Find the height of the Walk bar

Divide the Walk count by the class total, then multiply by 100.

Students in the first class

\(\displaystyle 40\)

Students in the second class

\(\displaystyle 30\)

Second class Walk bar

\(\displaystyle 40\%\)

A second class of 30 students is drawn on the same percentage scale. The Walk bar for the second class reaches 40%. How many students in the second class walk?

The bar is a share of the second class, not of the first

Tallest bar

\(\displaystyle 32\%\)

Tick step

\(\displaystyle 5\)

For this task, percentage-axis ticks are multiples of 5. Choose the smallest tick multiple at least one full step above the tallest bar, which reaches 32%

One full step above 32 is 37. Choose the smallest multiple of 5 that reaches at least 37.

A chart’s tallest bar is 32%, and its axis runs from 0 to 35%. Is that axis always mathematically wrong?

A chart of favourite drinks is reordered alphabetically. Every drink keeps its own original frequency. Is the data now incorrect?

Frequencies

\(\displaystyle 14,10,6,10\)

Using the largest count as every bar height. One of these lines is right. Which one?

A frequency bar chart uses bar length to compare counts. Why normally start that scale at zero?

Produce and verify a bar chart

For an invented survey of 24 students, club choices are Design 7, Garden 5, Games 8 and Music 4. Produce a frequency bar chart with a title, labelled axes, a zero baseline, equal scale steps and separate bars

1. 1Use and justify technology Choose a bar or column chart function, explain why it suits these nominal categories, and create the chart. Record the source cells or lists, category and frequency assignments, chart type and axis settings. Inspect the tool’s defaults
2. 2Verify independently Check all four bar heights against the given counts and check their sum by hand. State one alternative sensible axis maximum and explain why your chosen maximum works. Do not assume every readable chart has a unique maximum
3. 3Communicate one conclusion Name the modal club, state its count and percentage, and decide whether the mode is a majority. Explain whether reordering the four labelled bars would change the data
4. 4Self-review Your drawing, report and use of an external tool are not automatically marked

Model response: Produce and verify a bar chart

Compare your saved response with this model. Other correct layouts, technology functions and explanations are possible

1. 1One complete chart Use the title “Club choices of 24 students”, horizontal axis Club, and vertical axis Number of students. Separate bars have heights Design 7, Garden 5, Games 8 and Music 4. A zero-to-10 scale with equal steps of 2 is suitable; zero to 12 with equal steps of 2 also works
2. 2One technology record Enter the four clubs and their counts in two columns. Select both columns, choose a column chart, assign club labels to the category axis and counts to the height axis, set the vertical minimum to 0 and maximum to 10, and add the title and axis labels. This displays category counts; a time-series line or histogram of numerical intervals would answer a different question
3. 3Independent checks The heights 7, 5, 8 and 4 match all four source rows and sum to 24. Check that the software has not included a Total row as a fifth category, connected the bars with a line, exchanged two labels or truncated the baseline
4. 4Conclusion Games is the mode: 8 of 24 students, or 33.3% to one decimal place. It is the largest category but is not a majority, which requires more than 50%. These nominal categories can be reordered if every label retains its own count
5. 5Self-review checklist Check the title, labels and units, separate bars, zero baseline, equal scale steps, all four heights, your tool record and rationale, independent total and a conclusion that distinguishes mode from majority

Model chart: Club choices of 24 students. Which conclusion follows from the complete chart?