Difference between mean and median are important to understand for statistical, mathematical and probability theory point of view. The main difference between mean and median is that mean is the average value of a set of numbers while median is the center value or mid-point of a set of numbers that shows the lower value before it and higher value after it.

#### Median

Relating to, located in, or extending toward the middle.

#### Mean

To be used to convey; denote

"'The question is,' said Alice, 'whether you can make words mean so many different things'" (Lewis Carroll).

#### Median

(Anatomy) Of, relating to, or situated in or near the plane that divides a bilaterally symmetrical animal into right and left halves; mesial.

#### Mean

To act as a symbol of; signify or represent

In this poem, the budding flower means youth.

#### Median

(Statistics) Relating to or constituting the middle value in a distribution.

#### Mean

To intend to convey or indicate

"No one means all he says, and yet very few say all they mean, for words are slippery and thought is viscous" (Henry Adams).

#### Median

A median point, plane, line, or part.

#### Mean

To have as a purpose or an intention; intend

I meant to go running this morning, but I overslept.

#### Median

The dividing area, either paved or landscaped, between opposing lanes of traffic on some highways. Also called regionally boulevard, mall, median strip, meridian, neutral ground.

#### Mean

To design, intend, or destine for a certain purpose or end

A building that was meant for storage.

A student who was meant to be a scientist.

#### Median

(Statistics) The middle value in a distribution, above and below which lie an equal number of values.

#### Mean

To have as a consequence; bring about

Friction means heat.

#### Median

A line that joins a vertex of a triangle to the midpoint of the opposite side.

#### Mean

To have the importance or value of

The opinions of the critics meant nothing to him. She meant so much to me.

#### Median

The line that joins the midpoints of the nonparallel sides of a trapezoid.

#### Mean

To have intentions of a specified kind; be disposed

They mean well but lack tact.

#### Median

A central vein or nerve, especially the median vein or median nerve running through the forearm and arm.

#### Mean

Lacking in kindness; unkind

The teacher was not being mean in asking you to be quiet.

#### Median

(geometry) A line segment joining the vertex of triangle to the midpoint of the opposing side.

#### Mean

Cruel, spiteful, or malicious

A mean boy who liked to make fun of others.

#### Median

(statistics) A number separating the higher half from the lower half of a data sample, population, or probability distribution. The median of a finite list of numbers can be found by arranging all the observations from lowest value to highest value and picking the middle one (e.g., the median of {3, 3, 5, 9, 11} is 5). If there is an even number of observations, then there is no single middle value; the median is then usually defined to be the mean of the two middle values.

#### Mean

Expressing spite or malice

Gave me a mean look.

#### Median

(US) The area separating two lanes of opposite-direction traffic; the median strip.

#### Mean

Tending toward or characterized by cruelty or violence

Mean streets.

#### Median

(anatomy) Situated in a middle, central, or intermediate part, section, or range of (something).

#### Mean

Extremely unpleasant or disagreeable

The meanest storm in years.

#### Median

In the middle of an organ, structure etc.; towards the median plane of an organ or limb.

#### Mean

Ignoble; base

A mean motive. ].

#### Median

(statistics) Having the median as its value.

#### Mean

Occupying a middle or intermediate position between two extremes.

#### Median

Being in the middle; running through the middle; as, a median groove.

#### Mean

Intermediate in size, extent, quality, time, or degree; medium.

#### Median

Situated in the middle; lying in a plane dividing a bilateral animal into right and left halves; - said of unpaired organs and parts; as, median coverts.

#### Mean

Something having a position, quality, or condition midway between extremes; a medium.

#### Median

A median line or point.

#### Mean

A number that typifies a set of numbers, such as a geometric mean or an arithmetic mean.

#### Median

The value below which 50% of the cases fall

#### Mean

The average value of a set of numbers.

#### Median

Relating to or constituting the middle value of an ordered set of values (or the average of the middle two in an even-numbered set);

The median value of 17, 20, and 36 is 20

The median income for the year was $15,000

#### Mean

(Logic) The middle term in a syllogism.

#### Median

Dividing an animal into right and left halves

#### Mean

Means (used with a sing. or pl. verb) A method, a course of action, or an instrument by which an act can be accomplished or an end achieved.

#### Median

Relating to or situated in or extending toward the middle

#### Mean

Money, property, or other wealth

You ought to live within your means.

#### Mean

Great wealth

A woman of means.

#### Mean

(transitive) To intend, to plan (to do); to have as one's intention.

I didn't mean to knock your tooth out.

I mean to go to Baddeck this summer.

I meant to take the car in for a smog check, but it slipped my mind.

The authors meant a challenge to the status quo.

#### Mean

(intransitive) To have as intentions of a given kind.

Don't be angry; she meant well.

#### Mean

To intend (something) for a given purpose or fate; to predestine.

Actually this desk was meant for the subeditor.

Man was not meant to question such things.

#### Mean

(transitive) To intend an ensuing comment or statement as an explanation.[https://www.lexico.com/en/definition/i_mean%20I%20mean]

Your reasoning seems needlessly abstruse, complex, and verbose for me. I mean, could you dumb it down for my sake?

#### Mean

To convey (a meaning).

#### Mean

(transitive) To convey (a given sense); to signify, or indicate (an object or idea).

The sky is red this morning—does that mean we're in for a storm?

#### Mean

(transitive) Of a word, symbol etc: to have reference to, to signify.

What does this hieroglyph mean?

#### Mean

(transitive) Of a person (or animal etc): to intend to express, to imply, to hint at, to allude.

I'm afraid I don't understand what you mean.

He is a little different, if you know what I mean.

#### Mean

(transitive) To have conviction in (something said or expressed); to be sincere in (what one says).

Does she really mean what she said to him last night?

Say what you mean and mean what you say.

#### Mean

(transitive) To cause or produce (a given result); to bring about (a given result).

One faltering step means certain death.

#### Mean

(usually with to) To be of some level of importance.

That little dog meant everything to me.

Formality and titles mean nothing in their circle.

#### Mean

(obsolete) Common; general.

#### Mean

Of a common or low origin, grade, or quality; common; humble.

A man of mean parentage

A mean abode

#### Mean

Low in quality or degree; inferior; poor; shabby.

A mean appearance

A mean dress

#### Mean

Without dignity of mind; destitute of honour; low-minded; spiritless; base.

A mean motive

It was mean of you to steal that little girl's piggy bank.

#### Mean

Of little value or worth; worthy of little or no regard; contemptible; despicable.

#### Mean

Ungenerous; stingy; tight-fisted.

He's so mean. I've never seen him spend so much as five pounds on presents for his children.

#### Mean

Disobliging; pettily offensive or unaccommodating.

#### Mean

Intending to cause harm, successfully or otherwise; bearing ill will towards another.

Watch out for her, she's mean. I said good morning to her, and she punched me in the nose.

#### Mean

Powerful; fierce; strong.

It must have been a mean typhoon that levelled this town.

#### Mean

(colloquial) Accomplished with great skill; deft; hard to compete with.

Your mother can roll a mean cigarette.

He hits a mean backhand.

#### Mean

Difficult, tricky.

This problem is mean!

#### Mean

Having the mean (see noun below) as its value; average.

The mean family has 2.4 children.

#### Mean

(obsolete) Middling; intermediate; moderately good, tolerable.

#### Mean

A method or course of action used to achieve some result.

#### Mean

An intermediate step or intermediate steps.

#### Mean

Something which is intermediate or in the middle; an intermediate value or range of values; a medium.

#### Mean

The middle part of three-part polyphonic music; now specifically, the alto part in polyphonic music; an alto instrument.

#### Mean

(statistics) The average of a set of values, calculated by summing them together and dividing by the number of terms; the arithmetic mean.

#### Mean

(mathematics) Any function of multiple variables that satisfies certain properties and yields a number representative of its arguments; or, the number so yielded; a measure of central tendency.

#### Mean

(mathematics) Either of the two numbers in the middle of a conventionally presented proportion, as 2 and 3 in 1:2=3:6.

#### Mean

To have in the mind, as a purpose, intention, etc.; to intend; to purpose; to design; as, what do you mean to do?

What mean ye by this service ?

Ye thought evil against me; but God meant it unto good.

I am not a SpaniardTo say that it is yours and not to mean it.

#### Mean

To signify; to indicate; to import; to denote.

What mean these seven ewe lambs ?

Go ye, and learn what that meaneth.

#### Mean

To have a purpose or intention.

#### Mean

Destitute of distinction or eminence; common; low; vulgar; humble.

The mean man boweth down, and the great man humbleth himself.

#### Mean

Wanting dignity of mind; low-minded; base; destitute of honor; spiritless; as, a mean motive.

Can you imagine I so mean could prove,To save my life by changing of my love ?

#### Mean

Of little value or account; worthy of little or no regard; contemptible; despicable.

The Roman legions and great Cæsar foundOur fathers no mean foes.

#### Mean

Of poor quality; as, mean fare.

#### Mean

Penurious; stingy; close-fisted; illiberal; as, mean hospitality.

#### Mean

Occupying a middle position; middle; being about midway between extremes.

Being of middle age and a mean stature.

#### Mean

Intermediate in excellence of any kind.

According to the fittest style of lofty, mean, or lowly.

#### Mean

Average; having an intermediate value between two extremes, or between the several successive values of a variable quantity during one cycle of variation; as, mean distance; mean motion; mean solar day.

#### Mean

That which is mean, or intermediate, between two extremes of place, time, or number; the middle point or place; middle rate or degree; mediocrity; medium; absence of extremes or excess; moderation; measure.

But to speak in a mean, the virtue of prosperity is temperance; the virtue of adversity is fortitude.

There is a mean in all things.

The extremes we have mentioned, between which the wellinstracted Christian holds the mean, are correlatives.

#### Mean

A quantity having an intermediate value between several others, from which it is derived, and of which it expresses the resultant value; usually, unless otherwise specified, it is the simple average, formed by adding the quantities together and dividing by their number, which is called an arithmetical mean. A geometrical mean is the nth root of the product of the n quantities being averaged.

#### Mean

That through which, or by the help of which, an end is attained; something tending to an object desired; intermediate agency or measure; necessary condition or coagent; instrument.

Their virtuous conversation was a mean to work the conversion of the heathen to Christ.

You may be able, by this mean, to review your own scientific acquirements.

Philosophical doubt is not an end, but a mean.

By this means he had them more at vantage.

What other means is left unto us.

#### Mean

Resources; property, revenue, or the like, considered as the condition of easy livelihood, or an instrumentality at command for effecting any purpose; disposable force or substance.

Your means are very slender, and your waste is great.

#### Mean

A part, whether alto or tenor, intermediate between the soprano and base; a middle part.

The mean is drowned with your unruly base.

#### Mean

A mediator; a go-between.

He wooeth her by means and by brokage.

If by any means I might attain to the resurrection of the dead.

The wine on this side of the lake is by no means so good as that on the other.

#### Mean

An average of n numbers computed by adding some function of the numbers and dividing by some function of n

#### Mean

Mean or intend to express or convey;

You never understand what I mean!

What do his words intend?

#### Mean

Have as a logical consequence;

The water shortage means that we have to stop taking long showers

#### Mean

Denote or connote;

`maison' means `house' in French

An example sentence would show what this word means

#### Mean

Have in mind as a purpose;

I mean no harm

I only meant to help you

She didn't think to harm me

We thought to return early that night

#### Mean

Have a specified degree of importance;

My ex-husband means nothing to me

Happiness means everything

#### Mean

Intend to refer to;

I'm thinking of good food when I talk about France

Yes, I meant you when I complained about people who gossip!

#### Mean

Destine or designate for a certain purpose;

These flowers were meant for you

#### Mean

Approximating the statistical norm or average or expected value;

The average income in New England is below that of the nation

Of average height for his age

The mean annual rainfall

#### Mean

Characterized by malice;

A hateful thing to do

In a mean mood

#### Mean

Having or showing an ignoble lack of honor or morality;

That liberal obedience without which your army would be a base rabble

Taking a mean advantage

Chok'd with ambition of the meaner sort

Something essentially vulgar and meanspirited in politics

#### Mean

Excellent;

Famous for a mean backhand

#### Mean

Marked by poverty befitting a beggar;

A beggarly existence in the slums

A mean hut

#### Mean

Used of persons or behavior; characterized by or indicative of lack of generosity;

A mean person

He left a miserly tip

#### Mean

Used of sums of money; so small in amount as to deserve contempt

According to statistical and probability theory, median is a number is a set of number that works as a separator between lower and higher value, population, sample or a probability distribution. It is calculated by arranging the numbers from lowest value to highest value and then selecting the middle one. For example the data 4,10,8,2,5 will be first arranged from lower to higher value as 2,4,5,8,10 and then the middle value 5 will be chosen as the median. In case of even number, there is no single value, the median is them usually defined to be the mean of the two middle values (the median of 2,4,8,10) is (4+8)/2 = 6.

The definitions of mean varies in different field of study. It depends on the context. But the term mean is more related to state and probability theory. This term is used synonymously with expected value. Mean or arithmetic mean is a type of average that shows the average value of a set of number. It is calculated by adding up the all numbers and then dividing the result by the total numbers. For example, the mean of 7,8,2,3,4,5 is calculated as adding up the 7+8+2+3+5+5 and dividing it by total numbers that are 6 that gives the result of 5. For a data set, the term mathematical expectation and average are also used as a synonym of arithmetic mean. The mean of a set of numbers is denoted by , pronounced as “x bar”.