5.3 The Mode — Most Frequent Value

5.3 The Mode — Most Frequent Value

Sometimes, neither the mean nor the median tells us the most useful summary. Imagine a shoe shop owner deciding how many pairs of each size to stock. She does not care about the "average" shoe size — she cares about the size that most customers buy. For such questions, we use a third representative value called the Mode^?.

Finding the Mode — A Worked Example

A shopkeeper records the shoe sizes sold in a day: 6, 7, 7, 8, 6, 7, 9, 7, 8, 10, 7, 6.

Counting how often each size appears:

Size 7 appears the most (5 times). So the mode = 7. The shopkeeper should stock extra pairs of size 7.

When to Use Mean, Median or Mode

Each measure highlights a different aspect of the data:

• Mean — balances all values; works best when data is evenly spread with no outliers.
• Median — the middle value; resists outliers; good for income, house prices, heights.
• Mode — the most common value; essential for categorical data and planning stock.

5.4 Reading Bar Graphs: From a Cricket Match

Have you ever missed watching a cricket match? You can catch up in a minute by looking at a graph! The graph below shows the runs scored per over in a 20-over match.

The horizontal line lists the overs starting from 1, and the vertical line indicates the runs scored in each over. The graph shows the number of runs scored per over as a double bar graph — each bar corresponding to a team. Let us call them the blue team (denoted by blue) and the red team (denoted by red). The scale used for the runs per over is 1 unit = 5 runs. The circles shown on top of the bars indicate that a wicket fell in that over.

5.5 Data Detective — Telling Tall Tales

We just recalled seeing data of two Grade 5 classrooms with heights of boys and girls in each class. There, the average height of girls was more than boys in one class and vice versa in the other class. The dot plots (School A and School B) show heights of boys and girls side by side for classes across 7 grades — the mean for each row is marked.

Looking at this data, you might wonder: "Why is there a considerable difference in heights in the same grades across these two schools?" "Where are these schools located?" "How tall are students in Grades 6 to 8 in my school?" "What is the average height of all students in general?"

We see that men are taller than women in general, but what about the heights of boys and girls? Are boys taller than girls? Well, just by looking at the data of one or two schools, we cannot generalise for all children in our country, or around the world. Let us look at some data based on a survey of heights of boys and girls of different ages in India over time.

Heights in India — 1989 to 2019

The table below shows the average heights (cm) of boys and girls from ages 5 to 19 — first column is boys' heights, second is girls' heights — in 4 snapshot years (1989, 1999, 2009, 2019).