Step 3: Describing shape (symmetry)

Now that you can identify peaks, the next step is describing the shape of the distribution. The key question here is: Is the distribution symmetrical or asymmetrical?

The mirror test

Imagine drawing a vertical line through the center of the distribution. Ask yourself:

"Do both sides look roughly like mirror images of each other?"

✓ Symmetrical

  • Both sides roughly mirror each other
  • Values spread evenly around the center
  • Left and right halves have similar shapes

✗ Asymmetrical (Skewed)

  • One side extends further than the other
  • A "tail" stretches in one direction
  • Left and right halves look different

Symmetrical

Frequency Value Range

Both sides mirror each other

Asymmetrical (Skewed)

Tail Frequency Value Range

One side has a longer "tail"

Figure 3. A symmetrical distribution (left) versus an asymmetrical distribution (right).

How to determine shape

  1. Find the peak (or center) of the distribution
  2. Mentally draw a vertical line through the center
  3. Compare the left side to the right side
  4. If they roughly mirror each other → Symmetrical
  5. If one side has a longer tail → Asymmetrical

Example 1

Looking at this distribution, is it symmetrical or asymmetrical?

  • The peak is on the left side
  • The bars gradually decrease toward the right
  • There is a longer "tail" extending to the right
  • The left and right sides are NOT mirror images

Answer: "The distribution has an asymmetrical shape."

Example 2

Looking at this distribution, is it symmetrical or asymmetrical?

  • The peak is in the center
  • The bars gradually decrease toward both sides equally
  • There is no extended "tail" in either direction
  • The left and right sides ARE mirror images

Answer: "The distribution has a symmetrical shape."

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