Data Representation

Imagine being handed a list of 60 numbers. Spotting the largest, the smallest or any pattern would take ages. Now imagine the same data drawn as a chart — you can see the story in seconds.

That is the whole point of data representation: a good chart makes data quick to understand and easy to compare.

Whatever chart you draw, three things must always be there:

• A title — what is this chart about?
• Labels on both axes — what does each direction show?
• A clear, even scale — equal steps for equal amounts.

Without these, even a beautiful chart is hard to trust — a reader cannot tell what they are looking at.

A pictogram shows data using a picture or symbol. Each symbol stands for a fixed number of items, and a key tells you how many.

If one ⚽ stands for 4 goals, then 3 symbols means $3 \times 4 = 12$ goals. A part of a symbol shows a part of that amount — half a symbol would be 2 goals.

Pictograms are friendly and clear, but the key is everything. To find a total, count whole symbols, add on any parts, and multiply by the key value. To draw one, do the reverse: divide the frequency by the key value to find how many symbols to draw.

A bar chart uses bars of equal width to show frequencies. The height (or length) of each bar tells you how many — the taller the bar, the larger the frequency.

When the data is categorical or discrete, the bars have gaps between them, because the categories are separate.

To read a bar chart, trace the top of a bar across to the scale. To draw one, choose an even scale that fits your largest value, then make every bar the same width.

A bar chart makes comparisons instant — the tallest bar is the most common, the shortest is the least.

A line graph is the best choice when you want to show how something changes over time. Time goes along the bottom; the measurement goes up the side. Each reading is a point, and the points are joined with straight lines.

The shape of the line tells the story:

• A line going up means the value is increasing.
• A line going down means it is decreasing.
• A flat line means no change.
• A steep line means a fast change; a gentle slope means a slow change.

Line graphs are perfect for temperatures through a day, a plant's height over weeks, or a city's population over years.

A pie chart shows how a whole group is split into parts. The complete circle is everything; each slice is one category, and its size shows that category's share of the whole.

The key idea is fractions of a whole. If half the circle is one colour, that category is half — $\tfrac{1}{2}$ — of the group. A quarter slice is $\tfrac{1}{4}$ of the group.

So if 40 students were surveyed and the "walk" slice is half the circle, then $\tfrac{1}{2} \times 40 = 20$ students walk.

A pie chart is best when you want to show proportions — how the parts compare to the whole. It is not good for reading exact values, since you cannot do that without doing some calculation first.

Knowing how to draw and read charts connects to the whole of statistics — and far beyond:

• Collecting and organising data — once you have a frequency table, a chart is the natural next step.
• Averages and range — you will often read values straight off a chart, then calculate an average from them.
• Comparing groups — in science and geography you will use bar charts and line graphs to compare results and spot trends.
• In everyday life, charts are everywhere — news articles, sports results, weather apps and game statistics.

A chart is a powerful way to tell a story with data. Choose the right one, label it clearly, and you can make 60 numbers understandable at a glance.