Math Statistics: Mode, Median and Mean

In statistics, mode, median and mean are typical values to represent a pool of numerical observations. They are calculated from the pool of observations.

Mode is the most common value among the given observations. For example, a person who sells ice creams might want to know which flavour is the most popular.

Median is the middle value, dividing the number of data into 2 halves. In other words, 50% of the observations is below the median and 50% of the observations is above the median.

Mean is the average of all the values. For example, a teacher may want to know the average marks of a test in his class.

Mode

The mode of a set of observations is the value that occurs most frequently in the set. A set of observations may have no mode, one mode or more than one mode.

Example:

Find the mode of the following set of scores.

14 11 15 9 11 15 11 7 13 12

Solution:

The mode is 11 because 11 occurred more times than the other numbers

If the observations are given in the form of a frequency table, the mode is the value that has the highest frequency.

Example:

Find the mode of the following set of marks.

Solution:

The marks 2 and 3 have the highest frequency. So, the modes are 2 and 3.

Note: The above example shows that a set of observations may have more than one mode.

Example:

Find the mode for each of the following frequency tables:

The frequency table below shows the weights of different bags of rice.

There are 8 number cards with values 0 – 7. Each time a card is drawn at random and the card value is recorded. The frequency refers to the number of times a value is shown.

Solution:

a) Mode: 75 kg (highest frequency of 12)
b) Mode: 5 (highest frequency of 13)

Example:

The following frequency table shows the marks obtained by students in a quiz. Given that 4 is the mode, what is the least value for x?

Solution:

x is as least 12
(if x is less than 12 then 4 will not be the mode)

The following video shows you how to find the mode.

The following video shows how to calculate the mode, median and mean.

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