## Mode

Mode is defined as the term that repeats most number of times.

Or Mode is defined to be the term with the highest frequency.

Frequency is the number of times an observation occurs in a data.

Example 1

What is the mode of the numbers 1, 2, 1, 3, 3, 1, 2, 1?

1 repeats most number of times, i.e. 1 has the highest frequency.

So, mode of the above numbers is 1.

Example 2

What is the mode of the numbers 1, 2, 3, 2, 3, 1?

All three terms, 1, 2 and 3 are considered to be Mode, as each one repeats equally most number of times, or each one has the same highest frequency.

Example 3:

What is the mode of the numbers 1, 2, 3, 4, 5?

For the given numbers Mode does not exist.

We also say, mode is not defined.

Empirical Formula for Mode:

Mode = 3 Median – 2 mean

Example 1

What is the mode of certain numbers in which mean is 5 and median is 6?

Solution:

Apply

Mode = 3 Median – 2 mean

Mode = 3 × 6 – 2 × 5 = 18 – 10 = 8

Example 2

What value is mode greater than median, if median is 2 greater than mean?

Solution:

Since median is 2 greater than mean, so write the equation

Median – mean = 2.

To find “Mode is how much greater than median” is to find

Mode – median.

Let us rewrite the empirical formula

Mode = 3 Median – 2 mean, as

Mode – median = 2 median – 2 mean, i.e.

Mode – median = 2 × (median – mean)

Mode – median = 2 × 2 = 4. {as median – mean = 2}

So, mode is 4 greater than median