The modal class

The mode is the most common value. A grouped table hides the single values. It shows only a count for each class.

The lean

Here are 45 made-up readings, in minutes played.

The class 30-40 has the highest frequency, 15. It is the modal class. The mode is a number inside it. The neighbours decide where. They are the classes just before and just after it. The class below has 11 and the class above has 9. The lower neighbour is taller. So the mode leans down: it sits nearer 30 than 40.

The formula has five letters. l = 30 is the lower bound of the modal class. f₁ = 15 is its frequency. f₀ = 11 is the frequency of the class before it. f₂ = 9 is the frequency of the class after it. h = 10 is the class width. All classes must have the same width.

Mode = l + ((f₁ − f₀) ÷ (2f₁ − f₀ − f₂)) × h.

Mode = 30 + ((15 − 11) ÷ (30 − 11 − 9)) × 10 = 34.

Step by step: 15 − 11 = 4. And 2 × 15 − 11 − 9 = 10. Then 4 ÷ 10 × 10 = 4. So 30 + 4 = 34.

The modal class is the class with the highest frequency. Mode = l + ((f₁ − f₀) ÷ (2f₁ − f₀ − f₂)) × h.

If two classes tie for the highest frequency, the data is bimodal. Such a table has no single modal class.

Slide f₂ and watch the mode move.

Try the lab to finish this lesson.