Dot plots for counts and measurements
Each dot represents one recorded observation. A dot plot preserves individual recorded values, repeats and gaps on a common numerical scale
- Build Sort or tally the records, select a uniform numerical scale and place one dot at each recorded value
- Read Horizontal position gives the data value; vertical stack height gives its frequency
- Summarise Count every dot when locating the middle observation or pair. A mode is a value, and tied tallest stacks give tied modes
- Limits Rounding can merge positions. A plotted sample alone does not prove a claim about the whole population
Worked example
Times recorded to tenths of a second are 0.2, 0.3, 0.3, 0.6, 0.7 and 0.8. Describe the required stacks, median and range
- \(\displaystyle n=6\)Use six dots. The repeat at 0.3 is two observations
- \(\displaystyle f(0.2)=1,\quad f(0.3)=2\)Place one dot at 0.2 and two at 0.3
- \(\displaystyle f(0.6)=f(0.7)=f(0.8)=1\)Place one at each of these values. Preserve the empty 0.4 and 0.5 positions
- \(\displaystyle (0.3+0.6)/2=0.45\)The third and fourth observations determine the median, 0.45 seconds
- \(\displaystyle 0.8-0.2=0.6\)The range is 0.6 seconds
Common mistakes
Difficulty levels
Questions about this topic
Can dot plots show continuous measurements?+
Yes. Place each recorded measurement at its numerical value and state the recording precision and units
Must the horizontal axis start at zero?+
No. A dot is positioned on a number line, not measured as a bar length from a baseline. The scale must remain uniform and include all records
Must every numerical tick be labelled?+
No. Label enough regular ticks to make positions unambiguous. Do not remove the space occupied by values that have no observations
What does a stack mean?+
Its height is the frequency of the value directly below it. The individual dots represent separate observations
What if two stacks tie for tallest?+
Both values are modes, provided their frequency is greater than the other frequencies. If all values occur equally often, use the stated mode convention rather than inventing a unique mode
How is the median found?+
Order and count every observation. Use the middle value for an odd count or the average of the two middle values for an even count
What does rounding lose?+
It can combine different original measurements into one recorded position. The rounded plot does not reveal their original exact values
Does a sample plot describe everyone?+
It describes the plotted observations. Population conclusions also depend on how the sample was selected and on its limitations
Can I use a calculator?+
No. This topic is practised without a calculator
Which year level and chapter is this?+
Year 12, VCE Units 3 & 4, General Mathematics, chapter 1: Data distributions