Maths

Common mistakes in the mode

6 mistakes learners make with the mode, each one named and explained.

All common mistakes

The mode is the value that appears most often, not how often it appeared.

Any repeated value taken as the mode

What it looks like

You find a value that appears more than once and stop, without checking whether another appears more often.

Why it happens

The definition is remembered as the one that repeats rather than the one that repeats most.

A worked example

Question. 5, 8, 8, 2, 5, 8, 1

A common answer. 5, because it appears twice

The answer. 8, which appears three times

Why. Two of them repeat, so the counts have to be compared.

Put the two side by side

5 appears twice.
8 appears three times.

Count every value before choosing. The first repeat is not automatically the mode.

How often it appeared given instead of the value

What it looks like

You find the most common value correctly and then write down its count rather than itself.

Why it happens

The counting is the work, so the number you finish counting on feels like the answer.

A worked example

Question. 4, 8, 8, 10, 15

A common answer. 2, because 8 appeared twice

The answer. 8

Why. The mode is the value that appeared most, not the number of times it did.

Put the two side by side

The tally: 8 occurs twice.
The mode: 8.

The mode is always one of the values in the data. A count usually is not.

The largest value given as the mode

What it looks like

You pick the biggest number in the set as the mode.

Why it happens

Most is in the definition, and most sounds like biggest.

A worked example

Question. 4, 8, 8, 10, 15

A common answer. 15, the largest

The answer. 8

Why. Most often means most frequently, not largest.

Put the two side by side

Largest: 15, which appears once.
Most frequent: 8, which appears twice.

Count how many times each value appears. The mode never depends on size.

The mean given where the mode was asked for

What it looks like

You add and divide, and offer that as the mode.

Why it happens

All three averages are called averages, so any of them answers the word.

A worked example

Question. 4, 8, 8, 10, 15

A common answer. 9, the mean

The answer. 8, the mode

Why. The mode has to be a value that actually appears in the set.

Put the two side by side

The mean can be a number that is not in the data at all.
The mode is always one of the values you were given.

If your mode is not in the list, it is not a mode.

The median given where the mode was asked for

What it looks like

You order the list, take the middle, and give that as the mode.

Why it happens

Ordering the data is the habit built by median questions, and it carries over.

A worked example

Question. 4, 7, 7, 8, 10, 12, 12, 12, 15

A common answer. 10, the middle value

The answer. 12, which appears three times

Why. The middle of the list and the most common value are different questions.

Put the two side by side

Median: where a value sits.
Mode: how often it occurs.

Mode is a counting question. Tally the values and the answer is the tallest tally.

The smallest value given as the mode

What it looks like

You pick the smallest number in the set as the mode.

Why it happens

When the definition has not stuck, an extreme value is the easiest thing to point at.

A worked example

Question. 5, 8, 8, 2, 5, 8, 1

A common answer. 1, the smallest

The answer. 8, the most frequent

Why. 1 appears once, which makes it the least common value, not the most.

Put the two side by side

Smallest: 1.
Most frequent: 8.

The mode is about frequency only. Neither end of the range is relevant.

WAJD spots these patterns in your child's answers and names the one behind their wrong answers, instead of just marking them wrong.

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