Peaks and Valleys
Learn what it means when a histogram shows two tall bars instead of one, and how to read this kind of data correctly.
In the previous topic, we saw histograms that have one peak in the middle (symmetric) or one peak that leans to one side (skewed). But sometimes a histogram shows two peaks instead of one.
When a distribution has two clear peaks, we call it a bimodal distribution. The word "bi" means two, and "modal" comes from "mode" — the value that appears the most. So a bimodal distribution has two values (or two ranges) that are the most common.
One Peak (Unimodal)
The bars rise to one high point and then go down. Most values are close to that one peak.
Two Peaks (Bimodal)
There are two high points with a lower section between them. Values cluster in two ranges.
A bimodal histogram looks like two hills with a small valley between them.
When you see two peaks in a histogram, it usually means the data is made up of two different groups mixed together. Each group has its own typical values, and when they appear in the same chart, they create two peaks instead of one.
Common Reasons for Two Peaks
- Two different types of people or items are measured together (for example, men and women, or two product models).
- Two different time periods are mixed (for example, busy hours and quiet hours).
- Two different places are combined (for example, two schools or two branches).
Two peaks do not mean the data is wrong. It just means there are likely two groups inside the data, and we may need to study each group on its own.
Imagine a small restaurant in Cairo records the number of customers it has each hour from 11 a.m. to 11 p.m. for one week. Then it puts the data into a histogram, where the x-axis is the hour and the y-axis is the number of customers.
- A first peak around 1 p.m. — many customers come for lunch.
- A clear drop around 4 p.m. — fewer customers in the afternoon.
- A second peak around 8 p.m. — many customers come for dinner.
This is a bimodal distribution. The two peaks are not a mistake. They show that the restaurant has two busy times: lunch and dinner.
If the manager only looks at the average number of customers per hour, the result will be somewhere between the two peaks — for example, the afternoon hours. But the average alone hides the most important fact: the restaurant is very busy at two specific times and quiet between them.
When we see a bimodal distribution, the best step is usually to split the data into the two groups that are causing the two peaks, and then study each group separately.
How to Split the Data
- Look at the histogram and find the valley between the two peaks.
- Use that valley as a dividing line.
- All values to the left of the line belong to one group; all values to the right belong to the other group.
- Draw a histogram for each group on its own.
The valley is around 4 p.m. So we can split the day into:
- Lunch hours: 11 a.m. – 4 p.m.
- Dinner hours: 4 p.m. – 11 p.m.
After splitting, each group will have only one peak, and we can describe each one with its own average and shape.
Studying each group on its own gives a clearer picture than studying everything together. The manager can plan staff and food supplies for lunch and dinner separately.
In a bimodal distribution, the mean (average) often falls in the valley between the two peaks. This means the average is a value that does not really happen often.
A Simple Comparison
| Hour | Customers |
|---|---|
| 1 p.m. (lunch peak) | 40 |
| 4 p.m. (valley) | 10 |
| 8 p.m. (dinner peak) | 45 |
The average of these three hours is about 32 customers. But there is no single hour where the restaurant actually had 32 customers. The average alone does not describe the day correctly.
When data is bimodal, do not depend on the mean alone. Look at the histogram first, and report the two peaks separately when needed.
- A bimodal distribution has two clear peaks separated by a lower section.
- Two peaks usually mean the data contains two different groups mixed together.
- The best step is to split the data at the valley and study each group on its own.
- The mean can be misleading in a bimodal distribution because it often falls in the valley.
- Always look at the shape of the histogram before depending on a single average.