Mean, Median & Mode

What Are the Mean, Median, and Mode?

Mode

The mode is the number that appears most frequently in a data set.

• Example: The mode of {3, 7, 7, 2, 9} is 7.
• There can be more than one mode if several numbers appear with the same highest frequency.
• If all values are different, the data has no mode.

 

Median

The median is the middle value when the numbers are in numerical order.

• For an odd number of values, it's the middle number.
• For an even number, it's the average of the two middle values.
• Example: The median of {2, 4, 6, 8} is $\frac{4 + 6}{2} = 5$.

 

Mean

The mean is the arithmetic average:

Add up all the values.

Divide by how many values there are.

Example: The mean of {2, 4, 6} is \(\frac{2 + 4 + 6}{3} = 4.

 

When Should I Use Each One?

• Mean: Best when all values are fairly close together.
• Median: Better when there are outliers or extreme values.
• Mode: Useful for non-numerical data or finding most frequent values.

 

Example

A class recorded the number of books students read in a month:

Data: 3, 5, 7, 5, 9, 2, 4, 5, 6, 8

Find the:

(a) Mode

The most frequent value is 5 (appears 3 times).

\(\text{Mode} = 5\)

(b) Median

Step 1: Order the numbers: 2, 3, 4, 5, 5, 5, 6, 7, 8, 9

Step 2: Middle two values = 5 and 5

$\text{Median} = \frac{5 + 5}{2} = 5$

(c) Mean

$\text{Sum} = 2 + 3 + 4 + 5 + 5 + 5 + 6 + 7 + 8 + 9 = 54$

$\text{Mean} = \frac{54}{10} = 5.4$