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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 22 means the value 22 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 66 over the interval 10101919 means six values fell somewhere between 1010 and 1919.

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 10101919 bar holds six values, they could be six 1212s or one of each — the histogram alone can't say.

01234567860708090100Test scoreStudents

Which display to use

Dot plots shine for small data sets with a small range — quiz scores from 00 to 1010, books read in a month. Stacking 200200 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 11 dot above 22, 22 dots above 33, 44 dots above 44, 22 dots above 55, and 11 dot above 66. How many students took the quiz?

Each dot is one student, so add the stack heights1+2+4+2+11 + 2 + 4 + 2 + 1
Simplify1010

Answer: 1010 students took the quiz

Example 2: the most common value

Using the same dot plot — 11 dot above 22, 22 dots above 33, 44 dots above 44, 22 dots above 55, 11 dot above 66 — what is the most common score?

Find the tallest stack of dots
The stack above 44 has 44 dots, more than any other value

Answer: The most common score is 44

Example 3: reading a histogram bar

A histogram of ages at a park has bars: 0099 with height 33, 10101919 with height 66, 20202929 with height 44, and 30303939 with height 22. How many people are aged 10101919, and how many people are in the data set?

Read the height of the 10101919 bar66
For the total, add all the bar heights3+6+4+2=153 + 6 + 4 + 2 = 15

Answer: 66 people are aged 10101919; the data set has 1515 people

Try one yourself

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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 0099, 10101919, 20202929. Equal widths make heights honest: a taller bar always means more values.

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