What is the need of measuring central tendency in statistics?

What is the purpose of obtaining a measure of central tendency

Hi Greg,,Like to tell you I know ,but I dont , so Ill pass hopefully someone can help you, my guess would be that it is used as a medium to determine how things or people will react to certain situations, either way Im guessing, be well, my friend,( Everything real is given and received in silence.

) Meher Baba

When is the median the best measure of central tendency

It depends.

,If the data are caegorized and have no order, then there is no measure of central tendency as there is no center.

What is the center of Blonde, brown, red, white, black, bald?,If the data are categorized but ordered, then the mode makes sense.

,If the data are grouped continuous data (e.

g.

Income < $10,000, $10,000 - $19,000 etc) then the median can be calculated pretty closely in most cases and, sometimes, the mean can be as well (it depends on what the limits of the extreme categories are).

When is the mode the best measure of central tendency

It depends.

,If the data are caegorized and have no order, then there is no measure of central tendency as there is no center.

What is the center of Blonde, brown, red, white, black, bald?,If the data are categorized but ordered, then the mode makes sense.

,If the data are grouped continuous data (e.

g.

Income < $10,000, $10,000 - $19,000 etc) then the median can be calculated pretty closely in most cases and, sometimes, the mean can be as well (it depends on what the limits of the extreme categories are).

Which measure of central tendency is derived from the most common value

The term u201cmeasure of central tendencyu201d is used by statisticians and data analysts in connection with collections of data.

A synonym is u201cmeasure of central locationu201d.

,A measure of central tendency is,a single valuethat attempts to describe a collection of data,by identifying the central position within that collection of data.

,The idea is to determine what is u201ctypicalu201d or u201crepresentativeu201d.

For example, suppose you looked at the salaries of all employees in a particular job.

You might want to know what the typical employee is paid.

,There are three commonly used measures of central tendency:,Mode: the value that appears most oftenMedian: the value of the middle item, if you line them all up in order,Mean: the average of all the values,These three are not necessarily the same.

For example, suppose you went to a playground and saw seven children there, with the following ages:,1, 2, 2, 3, 4, 7, 9The mode (most frequent) age is 2.

,The median (middle) age is 3The mean or average age is the sum of all the ages divided by 7, which would be 4Calculation of average: (1+2+2+3+4+7+9) / 7 = 4,(you divide by 7 because there are 7 children),Note that sometimes people say u201caverageu201d but are really giving you the median or even the mode, rather than the mean.

,[The above example was derived from a discussion of this topic on Wikipedia].

,The following is a more detailed description that I found at SlideShare.

netIn what is called u201cnormally distributedu201d data, these three values are equal.

Many realistic collections of data are almost normally distributed, and in that case these three values are very similar.

However, many data collections are not normally distributed and in that case it is important to understand the differences among these three.

One of the most common mistakes people make in connection with central tendency measures is to confuse median and mean.

People also sometimes use one or the other to mislead.

You often see this with politicians or highly biased opinions from pundits, and it can very easily cause people to draw wrong conclusions.

,Here is an example.

,Suppose a company has ten workers.

Nine of them are paid $10 per hour.

The other one is paid $110 per hour.

Then the mode and the median are both $10 per hour, but the average is $20 per hour.

,Now suppose I say u201cthe median worker here is paid $10 per houru201d.

I might even say the u201caverageu201d worker is paid $10 per hour.

Either way, I am hiding the fact that one worker is paid a whole lot more.

,Or suppose I say u201cat my company the average pay is $20 per houru201d.

I am conveniently hiding the fact that the boss makes a whole lot more than that and everybody else makes only half of that.

,You will hear politicians and political pundits misusing these terms to mislead, so pay attention to what they are saying.

If a pundit says u201cthe average Starbucks worker is paid $20 per hour so why are they complaining?u201d, that pundit is hiding the fact that most of them get only $10 per hour and the boss is paid a whole lot more, which brings up the average.

,Another case where the term u201caverageu201d can mislead is when people talk about u201cbeating the stock market averageu201d.

The stock market average is actually a lot higher than the median (what the person in the middle makes) or the mode (what most people make).

I wonu2019t go into the details here, but the point is that u201cbeating the averageu201d is very unlikely when investing in stocks.

And the people claiming to have ways to do so are probably trying to sell you something that is very risky.

When the data has extreme scores, what is the best measure of average

I can give you two examples.

,He has the vocabulary of an emu.

He has a vocabulary of perhaps 200 words.

,Well, OK, a little hyperbole there, but he has the smallest vocabulary since the one-term presidency of Republican Herbert Hoover (1929-u201933) who, by the way, had the largest.

For those of you who havenu2019t yet realized it, Trumpu2019s is the smallest presidential vocabulary in the past century.

,Trump speaks at fourth-grade level, lowest of last 15 U.

S.

presidents, new analysis finds, 8 Jan.

2018, accessed 2020.

03.

18.

,His vocabulary is that of a 10-year-old 4th-grader.

Although, like many fourth-graders anxious to impress, he has piped up with, u201cI know words.

I have the best words.

u201d Donald J.

Trump Quotes , undated, accessed 2020.

03.

24.

,His best words are presumably his most frequently used.

These 10 are among his 20 most frequently used words: classy, amazing, terrific, winning, tough, loser, weak, smart, stupid, and bad.

Donald Trumps 20 Most Frequently Used Words, undated, accessed 2020.

03.

24.

,By every metric and methodology tested, Donald Trumps vocabulary and grammatical structure is [sic.

] significantly more simple, and less diverse, than any President since Herbert Hoover, when measuring u2018off-scriptu2019 words, that is, words far less likely to have been written in advance for the speaker, Donald Trump Unabridged - Speeches, Tweets, Interviews.

u2018The gap between Trump and the next closest president .

.

.

is larger than any other gap u2026.

u2019nId.

,Heu2019s u201cdumb as shit.

u201dFormer Secretary of Defense Jim Mattis said Trump had the understanding of a u201cfifth- or sixth-grader.

u201d Former national security adviser H.

R.

McMaster called him an idiot with the intelligence of a kindergartener.

Former Secretary of State Rex Tillerson called him a fucking moron.

Former White House chief of staff John Kelly said he was an u201cidiotu201d and that he was u201cunhinged.

u201d And, former National Economic Counsel chief Gary Cohn said he was u201cdumb as shit.

u201d,And, from Adam Carlsonu2019s comment, u201cLetu2019s not forget his college professor William Kelley who said u2018Donald Trump was the dumbest goddamn student I ever had.

u2019u201d,I venture to say that no other president has had any of that said of him.

,Trump demurred, saying that heu2019s a u201cvery stable geniusu201d and u201clike, really smart.

u201d Donald Trump speaks at the level of an 8-year-old, analysis finds, 9 Jan.

2018, accessed 2020.

03.

24.

He believes heu2019s u201cextremely intelligent.

u201d At various times, heu2019s tweeted that his IQ is u201cmuch higheru201d than Barack Obama and George W.

Bush.

Heu2019s even boasted that it is higher than comedian Jon Stewart and Lord Sugar, British star of The Apprentice.

(What is Donald Trumps IQ? | BBC, 11 Oct.

2017, accessed 2020.

03.

18.

) Which may be saying little.

,Yet, Theres something very striking about the incumbents insistence that he is both very stable and extremely intelligent, said Professor Dean Keith Simonton of Trump.

It comes across as very defensive, like hes discussing aspects of his person about which he feels vulnerable.

Who was the smartest president? It probably isnt Trump | Newsweek, 8 Jan.

2018, accessed 2020.

03.

18.

,Professor Fred I Greenstein, professor of politics emeritus at Princeton University, lists six qualities that bear on presidential performance.

,They are: public communication, political skill, organizational capacity, vision, cognitive style, and emotional intelligence.

,Trump scores low on emotional intelligence, cognitive style, vision, and organizational capacity.

What is Donald Trumps IQ? | BBC, 11 Oct.

2017, accessed 2020.

03.

18.

,He has little interest in reading, and prefers bullet points to paragraphed material.

Who was the smartest president? It probably isnt Trump | Newsweek, 8 Jan.

2018, accessed 2020.

03.

18.

,In his book Fire and Fury, journalist Michael Wolff reports a former campaign adviser, Sam Nunberg, as saying that he tried to teach Trump the Constitution.

u201cI got as far as the Fourth Amendment, before his finger is pulling down on his lip and his eyes are rolling back in his head.

When explaining the Constitution to Trump, an adviser says he only got as far as the Fourth Amendmentu201d | Newsweek, 3 Jan.

2018, accessed 2020.

04.

28.

,Of the 44 presidents prior to Trump, 17 have been Phi Beta Kappa members.

Bill Clinton, George H.

W.

Bush, and Jimmy Carter were the most recent.

Woodrow Wilson was the countryu2019s only Ph.

D.

president.

,Somehow, itu2019s difficult imagining Trump keeping up with such erudite and illustrious company.

,,Edit:n2020.

04.

10,Reading through the comments, I notice that a couple of common themes appear.

I think these particular ones worthy of a response in the answer itself.

,You.

Several comments use the personal pronoun u201cyou,u201d meaning me, the OP.

,I point out that, excepting the second, third, and ultimate paragraphs (one sentence paragraphs), nothing in the answer is something I wrote.

What I did was read through several news articles on point, glean from them the relevant content, and format and sequence that content into this answer.

,All of the answer, excepting those three paragraphs, is something reported in original sources that I found.

I included citations to those sources when quoted; when not quoted, I provided links to them where the text warranted.

,Those commenters who seem to think that I authored that content are mistaken in their understanding.

,Emus.

There were a couple of comments on my u201cvocabulary of an emuu201d statement that I appreciate: u201cIu2019m impressed u2014 you managed to insult emus, u201d (Bob Purcell); u201cI think you need to apologise [sic] to every emu in the worldu201d (User-13161724163322447903).

,Trump can get the job, he just canu2019t perform it.

The answer references the remarks of Harvard Professor Greenstein who gives the six qualities that bear on presidential performancepublic communication,political skill,organizational capacity,cognitive style,emotional entellegence,vision,Trump admittedly scores high on the first two qualities.

He fails miserably at the remaining 2/3rds of the qualifying criteria.

,The point being that he was very good at getting the job, he just can not perform it.

,Misuse of the Flesch-Kincaid Scale.

Representative of the comments making this point are these two:,Nathan Whitmore:,[T]he Flesch-Kincaid scores are not an index of language ability or intelligenceu2014they measure how difficult it is to read a text.

,T Michael Lutas:,u201cWhy are you misusing the Flesch-Kinkaid grade level evaluations? Theyu2019re not a measure of intelligence.

,u2026,The FK tests are intended to rate readability and the grade score is set as it is as an aid for people in the education field so that they may understand what is being conveyed better.

,This use of the F-K scale was discussed by Emily Shugerman New York @eshugerman in her piece for the British Newspaper The Independant, titled Donald Trump speaks at the level of an 8-year-old, analysis finds | Independt.

co.

uk, 9 Jan.

2018, accessed 2020.

04.

10.

,For those interested enough to read it, the piece in its entirety appears in Footnote 1.

,That piece begins:,An analysis of the Presidents first 30,000 words uttered in office found Mr Trump speaks at a third- to seventh-grade reading level u2013 lower than any other President since 1929.

Mr Trumpu2019s vocabulary and grammatical structure is u201csignificantly more simple, and less diverseu201d than any President since Herbert Hoover, the analysis found.

,The analysis referred to is Donald Trump Unabridged - Speeches, Tweets, Interviews by Fact Base CEO Bill Frischling.

It is,based on interviews, speeches and press conferences for every president dating back to 1929, compiled by online database Donald Trump Unabridged - Speeches, Tweets, Interviews.

Analysts at Fact Base studied the u201coff-scriptu201d remarks of all 15 men u2013 essentially, everything but their prepared speeches u2013 to compare and contrast their speaking skills.

,Analysts ran the records through eight different tests for vocabulary complexity, diversity, and comprehension level.

In every single test, Mr.

Trump scored the lowest.

Mr.

Trump averaged significantly fewer syllables per word than the last 14 Presidents, and used significantly fewer unique words.

The gaps appeared when comparing all available remarks, and when comparing only the first 30,000 words of each presidency.

Social media posts were excluded from the data.

n(emphasis mine),It would appear that the F-K Scale was not misused.

The analystsu2019 conclusion is based not just on an F-K Scale test but rather on eight different tests, a fact not stated in this answeru2019s original text.

(For which I am responsible.

),The result found is echoed by commenter Dan Lenski:,What seems to me most striking about Trumps speech is how disfluent and garbled it is, not his choice of words.

The man hardly ever utters anything that could be considered a complete sentence; he barely makes it through a stream of 10 consecutive words without either adhering to a tired formula or platitude, or veering off into the void both grammatically and conceptually.

,u2026,With Trump, its just incoherent streams of grievance and tangents and incomprehensible word salad every time he opens his mouth.

Its uncanny and weird on the rare occasions where he responds to a spontaneous question with a few sentences that arent filled with tangents and recycled tropes and filler words.

,Edit:n2020.

04.

07nJeez people.

I had no thought when I wrote this that it would be so well received.

To the many viewers, upvoters, and sharers, my sincere thanks.

I am gratified that you appreciate it.

,,Footnote 1:Trump speaks at level of 8-year-old, new analysis findsMr.

Trump scores the lowest of any of the past 15 presidentsEmily Shugerman New York @eshugermanTuesday 9 January 2018 16:57 nDonald Trump speaks at the level of an 8-year-old, analysis finds | Independt.

co.

uk, 9 Jan.

2018, accessed 2020.

04.

10,Donald Trump may call himself a genius on Twitter, but his spoken statements say otherwise.

,An analysis of the Presidents first 30,000 words uttered in office found Mr.

Trump speaks at a third- to seventh-grade reading level u2013 lower than any other President since 1929.

Mr.

Trumpu2019s vocabulary and grammatical structure is u201csignificantly more simple, and less diverseu201d than any President since Herbert Hoover, the analysis found.

,The comparison is based on interviews, speeches and press conferences for every president dating back to 1929, compiled by online database Donald Trump Unabridged - Speeches, Tweets, Interviews.

Analysts at Donald Trump Unabridged - Speeches, Tweets, Interviews studied the u201coff-scriptu201d remarks of all 15 men u2013 essentially, everything but their prepared speeches u2013 to compare and contrast their speaking skills.

,Analysts ran the records through eight different tests for vocabulary complexity, diversity, and comprehension level.

In every single test, Mr Trump scored the lowest.

,Mr.

Trump averaged significantly fewer syllables per word than the last 14 Presidents, and used significantly fewer unique words.

The gaps appeared when comparing all available remarks, and when comparing only the first 30,000 words of each presidency.

Social media posts were excluded from the data.

,u201cCompared to the 14 presidents who preceded him, by every measure, [Mr.

Trumpu2019s] use of words when off script are significantly less diverse, and simpler, than all presidents who preceded him back to Herbert Hoover,u201d wrote Donald Trump Unabridged - Speeches, Tweets, Interviews CEO Bill Frischling.

,The topic of Mr.

Trumpu2019s mental acuity has dominated the national conversation since the publication of Fire and Fury: Inside the Trump White House, an explosive new book about the Trump administration.

The booku2019s author, Michael Wolff, claims Mr.

Trumpu2019s family, friends, and co-workers all regularly questioned his fitness to serve.

,Mr.

Trump disputed these claims via Twitter last week, claiming he was a u201cvery stable geniusu201d and u201clike, really smartu201d.

He was supported by White House Press Secretary Sarah Huckabee Sanders, who called questions about the Presidentu2019s mental state u201coutrageousu201d.

,u201cIts absolutely outrageous to make these types of accusations and its simply untrue, and itu2019s sad that people are going and making these desperate attempts to attack the President,u201d she said in an interview on Fox & Friends.

,But many Congressional Democrats u2013 and even some of Mr.

Trumpu2019s fellow Republicans u2013 still refute the idea that the President is their intellectual superior.

More than a dozen House and Senate Republicans declined to endorse Mr.

Trumpu2019s claim that he was a u201cgeniusu201d in interviews with CNN on Monday.

,Republican Senator Jerry Moran, for example, said Mr.

Trump was u201csmart and capable at getting himself elected presidentu201d.

But when asked whether he was a genius, Mr.

Moran replied: u201cGot nothing.

u201d,