Dot Plots & Histograms
Dot plots and histograms both show how a data set is distributed along a number line — where the values pile up and where they thin out. The difference is how much detail they keep.
A dot plot shows one dot per data value, so you can recover every single number in the set. A histogram groups values into intervals and shows a bar over each one, so you know how many values landed in each interval but not exactly what they were.
Reading a dot plot
Each dot is one data value. Three dots stacked above the number means the value appears three times in the data set.
To find how many values are in the data set, count every dot. To find the most common value (the mode), look for the tallest stack. Because every value is visible, you can also compute the median or mean straight from the plot.
Reading a histogram
Each bar sits over an interval of values, and the bar's height tells how many values landed in that interval. A bar of height over the interval – means six values fell somewhere between and .
The bars touch each other on purpose — the intervals cover the number line with no gaps, so the bars have no gaps either. A bar chart of categories (favorite colors, pet types) keeps gaps between bars; a histogram of numbers does not. The histogram below groups test scores into intervals; notice the bars share edges.
The trade-off: a histogram can't tell you individual values. If the – bar holds six values, they could be six s or one of each — the histogram alone can't say.
Which display to use
Dot plots shine for small data sets with a small range — quiz scores from to , books read in a month. Stacking dots isn't practical.
Histograms shine for large data sets or a wide range of values — heights, ages at a park, salaries. Grouping into intervals keeps the picture readable at any size.
Worked examples
Example 1: counting data values in a dot plot
A dot plot of quiz scores shows dot above , dots above , dots above , dots above , and dot above . How many students took the quiz?
Answer: students took the quiz
Example 2: the most common value
Using the same dot plot — dot above , dots above , dots above , dots above , dot above — what is the most common score?
Answer: The most common score is
Example 3: reading a histogram bar
A histogram of ages at a park has bars: – with height , – with height , – with height , and – with height . How many people are aged –, and how many people are in the data set?
Answer: people are aged –; the data set has people
Try one yourself
Common questions
What's the difference between a histogram and a bar chart?
A histogram shows counts over numerical intervals, so the bars touch — the intervals share edges. A bar chart shows counts for separate categories like pizza vs. tacos, so the bars keep gaps. If the horizontal axis is a number line, it's a histogram.
Can I find the median from a histogram?
Only roughly. You can tell which interval the median falls in by counting bar heights until you pass the halfway point, but not its exact value — the histogram doesn't keep individual values. A dot plot gives you the exact median.
What does it mean if one stack or bar is much taller than the rest?
That value or interval is where the data piles up — a cluster. It usually contains the mode and pulls the center of the data toward it. Gaps and lonely dots far from the pile are worth noticing too; those are potential outliers.
Do histogram intervals have to be the same width?
At this level, yes — every histogram you'll read uses equal-width intervals like –, –, –. Equal widths make heights honest: a taller bar always means more values.
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