Mean vs. Expectation — What's the Difference?
Edited by Tayyaba Rehman — By Fiza Rafique — Updated on September 28, 2023
Mean refers to the average of a set of numbers, while Expectation is the anticipated value in probability and statistics. Both involve averages, but Expectation is specific to probable outcomes.
Difference Between Mean and Expectation
Table of Contents
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Key Differences
Both Mean and Expectation are concepts central to the study of statistics, but they have distinct interpretations. Mean, often synonymous with average, represents the sum of values divided by the count of those values. When you calculate the Mean, you are simply finding the central value of a dataset.
Expectation, on the other hand, is steeped more deeply in probability theory. It is the average or mean value of a random variable, taking into consideration the probabilities of different outcomes. Thus, Expectation doesn't merely capture a central value but integrates the likelihood of various scenarios.
An example can help illustrate the distinction between Mean and Expectation. Consider rolling a six-sided die. The Mean of all sides of the die is 3.5, a simple average of numbers 1 through 6. However, the Expectation would also be 3.5 because each side has an equal chance of landing, and when you consider the weighted average based on this probability, you arrive at the same value.
Comparison Chart
Definition
Average of a set of numbers.
Anticipated value considering probabilities of outcomes.
Context
General arithmetic.
Probability and statistics.
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Calculation
Sum of values divided by count.
Weighted average based on probabilities.
Dependency
Data values only.
Both data values and their associated probabilities.
Example
Mean of [1,2,3] is 2.
Expectation of a fair six-sided die roll is 3.5.
Compare with Definitions
Mean
Central value in a dataset.
The Mean age in the classroom was 15 years.
Expectation
A probable average in statistics.
The Expectation of a game's outcome was 3 points.
Mean
A value representing a set's midpoint.
The Mean salary at the company is $50,000.
Expectation
Anticipated value based on likelihoods.
The lottery's Expectation was lower than the ticket price.
Mean
There are several kinds of mean in mathematics, especially in statistics: For a data set, the arithmetic mean, also known as average or arithmetic average, is a central value of a finite set of numbers: specifically, the sum of the values divided by the number of values. The arithmetic mean of a set of numbers x1, x2, ..., xn is typically denoted by x ¯ {\displaystyle {\bar {x}}} .
Expectation
Foreseen average result of a random experiment.
The Expectation of the investment's return was 6%.
Mean
Intend to convey or refer to (a particular thing); signify
I don't know what you mean
I meant you, not Jones
He was asked to clarify what his remarks meant
Expectation
The act of expecting.
Mean
Intend (something) to occur or be the case
It was meant to be a secret
They mean no harm
Expectation
Eager anticipation
Eyes shining with expectation.
Mean
Have as a consequence or result
The proposals are likely to mean another hundred closures
Heavy rain meant that the pitch was waterlogged
Expectation
The state of being expected.
Mean
Unwilling to give or share things, especially money; not generous
They're not mean with the garlic
She felt mean not giving a tip
Expectation
Something expected
A result that did not live up to expectations.
Mean
Unkind, spiteful, or unfair
I was mean to them over the festive season
Expectation
Expectations Prospects, especially of success or gain.
Mean
(especially of a place) poor in quality and appearance; shabby
Her home was mean and small
Expectation
The expected value of a random variable.
Mean
Very skilful or effective; excellent
She dances a mean tango
He's a mean cook
Expectation
The mean of a random variable.
Mean
(of a quantity) calculated as a mean; average
Participants in the study had a mean age of 35 years
Expectation
The act or state of expecting or looking forward to an event as about to happen.
Mean
Equally far from two extremes
Hope is the mean virtue between despair and presumption
Expectation
That which is expected or looked for.
Mean
The value obtained by dividing the sum of several quantities by their number; an average
Acid output was calculated by taking the mean of all three samples
Expectation
The prospect of the future; grounds upon which something excellent is expected to occur; prospect of anything good to come, especially of property or rank.
Mean
A condition, quality, or course of action equally removed from two opposite extremes
The measure expresses a mean between saving and splashing out
Expectation
The value of any chance (as the prospect of prize or property) which depends upon some contingent event.
Mean
To be used to convey; denote
"'The question is,' said Alice, 'whether you can make words mean so many different things'" (Lewis Carroll).
Expectation
(statistics) The first moment; the long-run average value of a variable over many independent repetitions of an experiment.
Mean
To act as a symbol of; signify or represent
In this poem, the budding flower means youth.
Expectation
(colloquial statistics) The arithmetic mean.
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).
Expectation
The leaving of a disease principally to the efforts of nature to effect a cure.
Mean
To have as a purpose or an intention; intend
I meant to go running this morning, but I overslept.
Expectation
The act or state of expecting or looking forward to an event as about to happen.
My soul, wait thou only upon God, for my expectation is from him.
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.
Expectation
That which is expected or looked for.
Why our great expectation should be calledThe seed of woman.
Mean
To have as a consequence; bring about
Friction means heat.
Expectation
The prospect of the future; grounds upon which something excellent is expected to happen; prospect of anything good to come, esp. of property or rank.
His magnificent expectations made him, in the opinion of the world, the best match in Europe.
By all men's eyes a youth of expectation.
Mean
To have the importance or value of
The opinions of the critics meant nothing to him. She meant so much to me.
Expectation
The value of any chance (as the prospect of prize or property) which depends upon some contingent event. Expectations are computed for or against the occurrence of the event.
Mean
To have intentions of a specified kind; be disposed
They mean well but lack tact.
Expectation
The leaving of the disease principally to the efforts of nature to effect a cure.
Mean
Lacking in kindness; unkind
The teacher was not being mean in asking you to be quiet.
Expectation
Belief about (or mental picture of) the future
Mean
Cruel, spiteful, or malicious
A mean boy who liked to make fun of others.
Expectation
Wishing with confidence of fulfillment
Mean
Expressing spite or malice
Gave me a mean look.
Expectation
The feeling that something is about to happen
Mean
Tending toward or characterized by cruelty or violence
Mean streets.
Expectation
The sum of the values of a random variable divided by the number of values
Mean
Extremely unpleasant or disagreeable
The meanest storm in years.
Expectation
Mean value in probability theory.
The Expectation for the dice roll was 4.
Mean
Ignoble; base
A mean motive. ].
Expectation
Weighted average considering probabilities.
Due to biased chances, the game's Expectation shifted.
Mean
Occupying a middle or intermediate position between two extremes.
Mean
Intermediate in size, extent, quality, time, or degree; medium.
Mean
Something having a position, quality, or condition midway between extremes; a medium.
Mean
A number that typifies a set of numbers, such as a geometric mean or an arithmetic mean.
Mean
The average value of a set of numbers.
Mean
(Logic) The middle term in a syllogism.
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.
Mean
Money, property, or other wealth
You ought to live within your means.
Mean
Great wealth
A woman of means.
Mean
To intend.
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
To lament.
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
Meantime; meanwhile.
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
Mean
The sum of values divided by their count.
The Mean of 4, 5, and 6 is 5.
Mean
Synonymous with average.
The Mean temperature today was 70°F.
Mean
A measure of central tendency.
The Mean score on the test was 85%.
Common Curiosities
Can Mean and Expectation be the same value?
In some scenarios, like a fair six-sided die roll, the Mean and Expectation are the same.
Is Expectation relevant for skewed probabilities?
Absolutely, Expectation considers all probabilities, even if they are skewed.
Is Mean only for numerical data?
Yes, Mean requires numerical data to calculate an average.
Does Expectation consider probable outcomes?
Yes, Expectation calculates the weighted average based on probabilities.
Why is Expectation important in statistics?
It provides insight into probable outcomes in uncertain scenarios.
Is Mean always a value from the dataset?
No, the Mean can be a value not present in the dataset.
Can the Mean be misleading?
Yes, especially when outliers skew the dataset, the Mean might not represent the central tendency accurately.
Can Mean be used in probability theory?
Mean is a type of average, but in probability theory, Expectation, a specific type of mean, is used.
Which is more complex: calculating Mean or Expectation?
Expectation can be more complex, especially when probabilities aren't uniform.
Is Expectation always a certain outcome?
No, Expectation is an average anticipated outcome; actual results can vary.
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Fiza RafiqueFiza Rafique is a skilled content writer at AskDifference.com, where she meticulously refines and enhances written pieces. Drawing from her vast editorial expertise, Fiza ensures clarity, accuracy, and precision in every article. Passionate about language, she continually seeks to elevate the quality of content for readers worldwide.
Edited by
Tayyaba RehmanTayyaba Rehman is a distinguished writer, currently serving as a primary contributor to askdifference.com. As a researcher in semantics and etymology, Tayyaba's passion for the complexity of languages and their distinctions has found a perfect home on the platform. Tayyaba delves into the intricacies of language, distinguishing between commonly confused words and phrases, thereby providing clarity for readers worldwide.
