Q.For each of the following sets of data, find the mode:

Mode: The Most Frequent Value

Imagine you ask a class of 30 students how many siblings they have. The answers come in: some say 0, many say 1, a few say 2, and one student says 4. If you had to pick one number that best represents "the typical number of siblings" in this class, which would you choose?

You might pick the number that appears most often. If 15 students said "1 sibling," then 1 is the most common answer. That's the mode — the value that occurs with the highest frequency in a data set.

The mode is the only measure of central tendency (alongside mean and median) that can be used for non-numerical data. If you survey favourite ice cream flavours and "chocolate" is named by 40% of people, chocolate is the mode. You can't calculate an average flavour, but you can find the most popular one.

Precise Definition

A data set can have:

• One mode (unimodal) — e.g., {2, 3, 3, 5, 7} → mode = 3
• Two modes (bimodal) — e.g., {1, 1, 2, 4, 4, 5} → modes = 1 and 4
• More than two modes (multimodal) — e.g., {a, a, b, b, c, c} → modes = a, b, c
• No mode — if every value appears exactly once, there is no mode. Example: {1, 3, 5, 7} has no mode.

How to Find the Mode

For ungrouped data, simply count frequencies. For grouped data (like a frequency table), the mode is the class interval with the highest frequency — called the modal class.

Example (grouped data):

The modal class is 20–30 because it has the highest frequency (18). The exact mode within that class can be estimated using a formula, but for most school-level questions, identifying the modal class is sufficient.

Why Mode Matters

The mode is useful when:

• You have categorical data (colours, brands, yes/no responses)
• You want to know the most common case, not the average
• The data has extreme outliers that would distort the mean

For example, if you're a shopkeeper stocking shoes, the mean shoe size might be 7.2, but the mode might be 8 — because more customers wear size 8 than any other single size. You'd stock more size 8 shoes.