Histogram shapes / Bell-shaped
Bell-Shaped Histogram (Normal Distribution)
A bell-shaped histogram is symmetric with a single central peak that tapers on both sides. See a normal-distribution example, the 68-95-99.7 rule, and how mean and median line up.
What a bell-shaped histogram looks like
A bell-shaped histogram is symmetric with one peak in the middle and bars that fall away evenly on both sides, tracing the outline of a bell. It is the picture of a normal distribution, the most common shape in statistics.
The example above is adult heights in inches. Most people are near the average, and the count drops off smoothly as you move toward the short and tall ends.
Mean, median, and mode line up
In a perfectly bell-shaped set the three averages sit on top of each other in the center:
mean = median = mode
Because the shape is symmetric, there is no tail to pull the mean off center. When those three numbers are close together in the stats panel, the data is close to normal.
The 68-95-99.7 rule
For a normal distribution, about 68 percent of values fall within one standard deviation of the mean, about 95 percent within two, and about 99.7 percent within three. That rule is why the standard deviation is so useful for bell-shaped data.
Where you see it
Heights, blood pressure, measurement error, and standardized test scores are all roughly normal. Paste your numbers into the histogram maker and compare the mean and median. If they nearly match and both sides taper evenly, you have a bell.
Frequently asked questions
- Is a bell-shaped histogram the same as a normal distribution?
- A bell shape is the visual signature of a normal distribution. Real data is rarely perfectly normal, but a symmetric single-peaked histogram with even tails is close enough to use normal-distribution rules like 68-95-99.7.
- Where are the mean and median on a bell-shaped histogram?
- Both sit at the center peak. Because the shape is symmetric, the mean, median, and mode all land in the same place.