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Mode and Median mess

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Joined: 27 Oct 2012
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11 Mar 2013, 13:14
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Hi! Great forum, found a lot of useful for me!

But still have one question. What are the exact definitions of Mode and Median?

Consider the following examples:

Mode
{1, 2, 2, 3, 3, 4, 4} What is mode? 2? 3? 4? Or maybe (2+3+4)/3?

Median
{-1, 0, 1} No problem, median is 0.

{1, 2, 3, 4} Is median (2+3)/2?

{1, 2, 2, 3, 3, 4} Here? 2, 3 or 2.5?

So misunderstanding can affect a solution. If somebody could make it clear, I'll appreciate it. Thanks!
Intern
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Re: Mode and Median mess [#permalink]

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11 Mar 2013, 14:12
Mode is the number that occur most often in the set of values. In this case, 2, 3 & 4 are mode.

To calculate the median, arrange the set of numbers in ascending order & then:
1) if the set has even numbers take the 2 values in the middle & calculate the mean.
2) if the set has odd numbers, the center value is the median.

gafych wrote:

Median
{-1, 0, 1} No problem, median is 0.

{1, 2, 3, 4} Is median (2+3)/2?

{1, 2, 2, 3, 3, 4} Here? 2, 3 or 2.5?

So misunderstanding can affect a solution. If somebody could make it clear, I'll appreciate it. Thanks!

In this case the medians are.

0. You are correct
(2+3)/2 You are correct
(2+3)/2 = 2.5 You are almost correct
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Re: Mode and Median mess [#permalink]

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12 Mar 2013, 07:07
Expert's post
gafych wrote:
Hi! Great forum, found a lot of useful for me!

But still have one question. What are the exact definitions of Mode and Median?

Consider the following examples:

Mode
{1, 2, 2, 3, 3, 4, 4} What is mode? 2? 3? 4? Or maybe (2+3+4)/3?

Median
{-1, 0, 1} No problem, median is 0.

{1, 2, 3, 4} Is median (2+3)/2?

{1, 2, 2, 3, 3, 4} Here? 2, 3 or 2.5?

So misunderstanding can affect a solution. If somebody could make it clear, I'll appreciate it. Thanks!

MODE
The mode is the number that occurs the most frequently in a data set. For example mode of the set {2, 3, 4, 4} is 4.

Set can have more than one mode, for example set {2, 2, 3, 3, 5} has two modes 2 and 3.

If every number in the set occurs an equal number of times, then the set has no mode. For example set {1, 2, 3} has no mode.

For example:

{1, 2, 4, 8, 8, 8, 9, 10, 10, 10, 11} - has two modes 8 and 10;

{1, 2, 3, 4, 5, 6} - has no mode, since every number in the set occurs an equal number of times;

{2, 2, 4, 4, 6, 6} - has no mode, since every number in the set occurs an equal number of times.

MEDIAN
The median of a set with odd # of terms is just a middle term (when ordered in ascending/descending order).

The median of a set with even # of terms is the average of two middle terms (when ordered in ascending/descending order).

Hope it helps.
_________________
Re: Mode and Median mess   [#permalink] 12 Mar 2013, 07:07
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