Display choice and information
Match the representation to the data and the statistical question. Explain what a display shows and what it leaves out
- Start with the question Choose a display for the variable and what the reader needs to find. The number of observations affects readability, but there is no universal sample-size cutoff
- Compare categories A bar chart compares category frequencies or percentages using separate bars. Ordinal categories retain their meaningful order
- Keep recorded values Dot plots show one dot per observation on a numerical scale. Stem-and-leaf plots retain recorded values using a stated place-value key. Both can represent measured or counted data
- Group numerical values Histograms show frequencies in numerical intervals. In an equal-width frequency histogram, column height gives frequency. Grouping hides the exact values within each interval
Worked example
A researcher has reaction times 0.21, 0.24, 0.31 and 0.38 seconds. They want to retain each recorded value using stems and leaves. Choose a display and give a key
- \(\displaystyle 2\mid1\ 4\)Use tenths as stems and hundredths as leaves: the first row records 0.21 and 0.24
- \(\displaystyle 3\mid1\ 8\)The second row records 0.31 and 0.38
- \(\displaystyle 2\mid4=0.24\text{ s}\)A stem-and-leaf plot with this key meets the requested format. A dot plot could also preserve these values for a different presentation aim
Common mistakes
Difficulty levels
Questions about this topic
Can measured data be shown in a dot plot?+
Yes. Each dot marks one recorded numerical value, including a continuous measurement rounded to the stated precision
Does sample size force one particular display?+
No. Size affects readability, but there are no universal cutoffs. Consider the statistical question, amount of detail, range, repeated values and available space
Can a small data set have a histogram?+
Yes, if grouping answers the question and the intervals are useful. With few observations, a dot plot may communicate the individual values more clearly
Can a stem plot show decimal measurements?+
Yes. State a key that assigns place value and units, such as 2 | 4 = 0.24 seconds. A unit change does not make a representation mathematically unavailable
What is lost when observations are grouped?+
Exact values within intervals are lost. The same grouped frequencies can come from many different raw data sets
Why do histogram columns touch?+
Adjacent columns represent adjoining numerical intervals. An empty interval can have zero height; that is not an arbitrary gap between categories
When does histogram height equal frequency?+
In the equal-width frequency histograms used here. With unequal-width intervals, a density scale is needed so column area represents frequency
Must categorical data always use a bar chart?+
No. A frequency table or another appropriate categorical display may suit the question. A bar chart is useful for comparing category frequencies or percentages visually
Can I use a calculator?+
No. This topic is practised without a calculator
Which year level and chapter is this?+
Year 10 Mathematics, chapter 5: Statistics