How do you choose the right way to show your data?
You can make perfectly correct calculations and still tell the story of your data badly if you pick the wrong display. A list of raw values is like a messy camera roll , everything is there, but you cannot spot the pattern quickly.
Start by deciding what kind of data you have, because that controls which diagrams make sense. Qualitative data is about labels or categories, like favourite sport or transport type.
Qualitative data gives descriptions rather than measurements, so you sort it into groups instead of treating it like numbers you can average.
Quantitative data is numerical.
Quantitative data is data you can record with numbers, such as time, mass, score, or temperature.
Inside this, you need one more split. Discrete data jumps between separate values, like number of siblings or goals scored.
Discrete data comes from counting, so there are gaps between possible answers.
Continuous data can sit anywhere in an interval, like height or distance.
Continuous data comes from measuring, so values can vary smoothly across a range.
A sneaky trap: if a continuous measurement is rounded, it does not become discrete. If your height is written as 162 cm, your actual height could still be 161.6 cm or 162.4 cm. The variable is still continuous underneath.
Once you know the type, your display choice gets easier. Categories and small sets of separate values work well in a frequency table. If your numerical data has loads of different values, especially measured data, you often group it into intervals instead.
A distribution is the overall look of your data set , where values tend to sit, how spread out they are, and whether there are gaps, clusters, or uneven tails.
Quick method for choosing a representation
- Decide whether your data is qualitative or quantitative.
- If it is quantitative, decide whether it is discrete or continuous.
- Use a frequency table for categories or separate values.
- Use grouped intervals when there are many possible values or measured data.
- Use a stem-and-leaf diagram, box plot, or cumulative frequency graph when you want to see the shape more clearly.
You survey 30 students about travel time to school. Because time is measured, your data is continuous. Since many different values are possible, a grouped frequency table is a sensible choice. If instead you asked for favourite music genre, that would be qualitative, so you would list categories in a frequency table rather than class intervals.
In real investigations, this first choice saves marks. If you try to draw a cumulative frequency curve for eye colour, it makes no sense because categories do not have a natural numerical order.
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