Histogram shapes / Symmetric
Symmetric Histogram (No Skew)
A symmetric histogram is a mirror image around its center, so the left and right halves match. See an example, why mean equals median, and how it relates to bell and uniform shapes.
What a symmetric histogram looks like
A symmetric histogram is a mirror image around its middle. Fold it down the center and the left half lands on top of the right half. There is no long tail on either side, so the data is not skewed.
The example above rises to a center and falls away at about the same rate on both sides.
Mean equals median
Symmetry is the reason the two main averages agree:
mean = median
With no tail to pull the mean off to one side, it settles at the same center point as the median. In practice, if the mean and median in the stats panel are very close, your data is close to symmetric.
Symmetric is a family, not one shape
Bell-shaped and uniform histograms are both symmetric. A bell has a central peak, a uniform shape is flat, and a triangular shape like the example rises to a point, but all three are mirror images around the center. Symmetric is the umbrella; skew is what breaks it.
Paste your numbers into the histogram maker and compare the mean and median. When they line up and neither tail runs long, the shape is symmetric.
Frequently asked questions
- What does it mean if a histogram is symmetric?
- The data is balanced around its center, with the left and right halves mirroring each other and no long tail on either side. The mean and median end up equal or very close.
- Are all symmetric histograms bell-shaped?
- No. A bell shape is one kind of symmetric histogram, but flat (uniform) and triangular shapes are symmetric too. Symmetry only means the two halves match, not that there is a single rounded peak.