The tallest bar

The idea

Data with more than one value of maximum frequency is multimodal; in grouped data the mode cannot be read from the frequencies, but the class with maximum frequency, the modal class, contains it.

Wickets in ten matches

A bowler took these numbers of wickets in 10 matches: 2, 6, 4, 5, 0, 2, 1, 3, 2, 3.

The mode is the value that occurs most often. Count each number and see which one wins.

Which number of wickets is the mode?

• 2
• 3
• 6

Find the tallest bar

With ungrouped data you count each value. In a grouped table you only know how many are in each class. Tap the bar of the class with the greatest frequency. Try all three tables. Watch the last one carefully.

The modal class

In grouped data the mode cannot be read from the frequencies. We find the class with the maximum frequency, the modal class. The mode is a value inside it.

In ungrouped data 2 occurs 3 times, more than any other number, so the mode is 2. In a grouped table every class holds many different values, so we can only point to a class. If more than one value (or class) has the maximum frequency, the data is multimodal. NCERT works only with problems that have a single mode.

Notes

The modal class is the class with the maximum frequency. The mode is a value inside it.

Check yourself

The heights of 51 girls are in classes with frequencies: below 140: 4, 140–145: 7, 145–150: 18, 150–155: 11, 155–160: 6, 160–165: 5. Which is the modal class?

The marks of 53 students in classes 0–10, 10–20, …, 90–100 have frequencies 5, 3, 4, 3, 3, 4, 7, 9, 7, 8. What is the frequency of the modal class?

Answer: 9

The largest frequency is 9, for the class 70–80.

Four classes have frequencies 3, 8, 8, 5. How many modal classes are there?

The modal class of the marks table is 40–55. Is the mode equal to its class mark, 47.5?

• 145–150 — correct. Yes! Its frequency, 18, is the greatest.
• 150–155. 11 is smaller than 18.
• Below 140. Its frequency is only 4.
• Two: the data is multimodal — correct. Yes! Two classes tie for the maximum frequency, 8.
• One: the first 8. Both classes with frequency 8 are modal classes. You cannot choose just one.
• None, because the 8s are equal. A class with the maximum frequency is a modal class, even when another class ties with it.
• Not necessarily. The mode is some value inside 40–55, and we find it with a formula. — correct. Yes! The class only tells us where the mode is. The next lesson finds the value.
• Yes, the mode is always the class mark. The class mark is the middle of the class. The mode depends on the frequencies of the neighbouring classes too, as you will see next.
• Yes, the mode is the frequency, 7. The frequency 7 tells how many students are in the class. The mode is a mark, a value of the data.