Tally Charts, Frequency Tables, Bar Charts and Pie Charts

1. From raw data to a frequency table

Raw data are the facts exactly as they were collected, in no special order. To make sense of them we count how many times each value occurs. We do this with a tally: go through the data once, and for every value draw one stroke in its row. After four strokes, the fifth is drawn across them like a gate, making bundles of five that are easy to count.

Here are the 30 test marks (out of 10) that Madam Akosua recorded:

7, 5, 6, 8, 7, 4, 6, 9, 5, 7, 6, 3, 8, 7, 5, 6, 4, 7, 10, 6, 5, 8, 7, 6, 2, 9, 7, 5, 6, 4.

1. 1Draw a table with three columns: Mark, Tally, Frequency.
2. 2List every possible mark in order from the smallest to the largest.
3. 3Go through the data once, and put a stroke in the correct row as you read each mark. Cross out the number in the list so that you do not count it twice.
4. 4Count the strokes in each row and write the frequency.
5. 5Add the frequencies. The total must equal the number of items in the raw data.

2. Bar charts

A bar chart shows a frequency table as a picture. Each value gets a bar, and the height of the bar is the frequency. Follow these rules so your chart can be read by anyone:

• Give the chart a title that says what it shows.
• Draw two axes. Label the horizontal axis (marks) and the vertical axis (number of learners).
• Use an equal-interval scale on the vertical axis, such as 0, 1, 2, 3, ... and start at zero.
• Draw all bars with the same width and equal gaps between them.
• Label each bar clearly.

▶ The tallest bars are the marks that most learners obtained (6 and 7). Look at the shape: most learners scored in the middle (5 to 7).

Now we can analyse the chart and write conclusions. The most common marks are 6 and 7, each obtained by 7 learners (we say the data have two modes). Only 1 learner got full marks. The number of learners who scored 8 or more is 6. We can also pose questions: Why did so few learners score below 4? What could help the learners with low marks?

A double bar chart puts two bars side by side for each category so that we can compare two groups, for example the rainfall of Kumasi and Oda in each month, or how Fakor spends his day compared with how you spend yours. Use two different colours and add a key.

3. Pie charts

A pie chart shows how a whole is shared. The whole circle has 360°. Each category gets a sector whose angle is its share of the total:

$$\text{angle}=\frac{\text{frequency}}{\text{total frequency}}\times 360^{\circ }$$

A group of learners recorded the number of people living in 40 households around their homes. The table shows the frequencies and the sector angles.

▶ Households with 4 people form the biggest sector. Notice that all the sectors together make a complete circle.

1. 1Find the total frequency.
2. 2Work out each angle: frequency ÷ total × 360°.
3. 3Check that the angles add up to 360°.
4. 4Draw a circle, then use a protractor to draw a radius and measure each angle one after the other.
5. 5Label each sector with its name and, if you like, its percentage.

4. Line graphs and drawing conclusions

A line graph is best when data change over time, such as rainfall every month, the price of tomatoes every week or the population of a town every ten years. Plot a point for each time period and join the points with straight lines. The rise and fall of the line shows the trend.

▶ The line rises to a peak in July (55 mm) then falls again. Line graphs show trends over time.

Choose the right graph for your data: use a bar chart to compare separate categories, a pie chart to show shares of a whole, and a line graph to show change over time. To analyse any graph, read the title and axes, find the largest and smallest values, compare, calculate totals or differences, and then write a sentence conclusion.

Worked examples

Try each one yourself first, then open the solution and compare every step.