Math Statistics: Mode, Median and Mean

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What Is 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 flavor 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.

The following diagrams show how to find the mean, median, mode and range. Scroll down the page for examples and solutions.

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.

Marks	1	2	3	4	5
Frequency	6	7	7	5	3

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.

Weight (kg)	45	50	55	60	65	70	75	80
Bags of rice (Frequency)	8	11	7	10	9	10	12	8

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.

Card values	0	1	2	3	4	5	6	7
Frequency	8	12	7	10	12	13	12	10

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?

Marks	1	2	3	4	5	6
Number of students (Frequency)	7	9	10	x	9	11

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

Mean, Median, Mode, Range, Interquartile Range

This lesson shows you how to find the mean, median, mode, range and interquartile range for a list of numbers.

Example:
Find the mean, median, mode, range and interquartile range for the following data.
5, 7, 9, 9, 10, 11, 11, 11, 12

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Frequency Table - Mean, Median, Mode, Range And Interquartile Range

This lesson shows you how to find the mean, median, mode, range and interquartile range from a frequency table.

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Mean, Mode And Median From Frequency Tables

How to find the mean, mode and median from a frequency table for both discrete and grouped data?

For grouped data:

• Mean: multiply midpoints by frequencies and add the sub-totals. Divide by the total of the frequencies.
• Mode: find the largest frequency - the corresponding value is the modal value or modal class.
• Median: calculate a running total of the frequencies - the first interval that is above half the total contains the median.

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