For this assignment read the news examples below and explain the concept behind

Question

For this assignment read the news examples below and explain the concept behind each example. Fine a sperate news source and explain how the concept from the news example applies to the concept you found. Find a separate news source/article and explain how the concept from the Well Chosen Average applies to the news/source you found

The Well-Chosen Average 31

primitive tribe is only five feet, you get a fairly good idea of

the stature of these people. You don't have to ask whether

that average is a mean, median, or mode; it would come out

about the same. (Of course, if you are in the business of

manufacturing overalls for Africans you would want more

information than can be found in any average. This has to

do with ranges and deviations, and we'll tackle that one in

the next chapter.)

The different averages come out close together when you

deal with data, such as those having to do with many human

characteristics, that have the grace to fall close to what is

called the normal distribution. If you draw a curve to rep-

resent it you get something shaped like a bell, and mean,

median, and mode fall at the same point.

Consequently one kind of average is as good as another

for describing the heights of men, but for decribing their

pocketbooks it is not. If you should list the annual incomes

of all the families in a given city you might find that they

ranged from not much to perhaps £20,000 or so, and you

might find a few very large ones. More than nine-five per

cent of the incomes would be under £5,000, putting them

way over towards the left-hand side of the curve. Instead of

being symmetrical, like a bell, it would be skewed. Its shape

would be a little like that of a child's slide, the ladder rising

sharply to a peak, the working part sloping gradually down.

The mean would be quite a distance from the median. You

can see what this would do to the validity of any com-

parison made between the 'average' (mean) of one year and

the 'average' (median) of another.

In the neighbourhood where I sold you some property the

two averages are particularly far apart because the dis-

tribution is markedly skewed. It happens that most of your

neighbours are small farmers or wage earners employed in a

near-by village or elderly retired people on pensions. But

32 How to Lie with Statistics

three of the inhabitants are millionaire week-enders and

these three boost the total income, and therefore the arith-

metical average, enormously. They boost it to a figure that

practically everybody in the neighbourhood has a good deal

less than. You have in reality the case that sounds like a

joke or a figure of speech: Nearly everybody is below

average.

That's why when you read an announcement by a cor-

poration executive or a business proprietor that the average

pay of the people who work in his establishment is so much,

the figure may mean something and it may not. If the aver-

age is a median, you can learn something significant from it:

Half the employees make more than that; half make less. But

if it is a mean (and believe me it may be that if its nature is

unspecified) you may be getting nothing more revealing than

the average of one £25,000 income - the proprietor's - and

the salaries of a crew of underpaid workers. 'Average annual

pay of £3,800' may conceal both the £1,400 salaries and

the owner's profits taken in the form of a whopping

salary.

How neatly this can be worked into a whipsaw device, in

which the worse the story, the better it looks, is illustrated

in some company statements. Let's try our hand at one in a

small way.

You are one of the three partners who own a small manu-

facturing business. It is now the end of a very good year.

You have paid out £99,000 to the ninety employees who do

the work of making and shipping the chairs or whatever it is

that you manufacture. You and your partners have paid

yourselves £5,500 each in salaries. You find there are profits

for the year of £21,000 to be divided equally among you.

How are you going to describe this? To make it easy to

understand, you put it in the form of averages. Since all the

employees are doing about the same kind of work for

I

£25,000

I

£7,600

II

£5,600

*

i3,472 Arithmetical average

III

£3,500

lit!

£2,500

II

£2,100 Median (the one In the middle.12 above him, 12 below)

9

Ei.400 Mode (occurs most frequently)

34 How to Lie with Statistics

similar pay it won't make much difference whether you use

a mean or a median. This is what you come out with:

Average wageofemployees £1,100

Average salary and profit of owners 12,500

That looks terrible, doesn't it? Let's try it another way. Take

£15,000 of the profits and distribute it among the three part-

ners as bonuses. And this time when you average up the

wages, include yourself and your partners. And be sure to

use a mean.

Average wage or salary £1,403

Average profit of owners 2,000

Ah. That looks better. Not as good as you could make it

look, but good enough. Less than six per cent of the money

available for wages and profits has gone into profits, and you

can go further and show that too if you like. Anyway,

you've got figures now that you can publish, post on a bul-

letin board, or use in bargaining.

This is pretty crude because the example is simplified, but

it is nothing to what has been done in the name of account-

ing. Given a complex corporation with hierarchies of em-

ployees ranging all the way from beginning typist to

president with a several-hundred-thousand-dollar bonus, all

sorts of things can be covered up in this manner.

So when you see an average-pay figure, first ask: Average

of what? Who's included? The United States Steel Cor-

poration once said that its employees' average weekly

earnings went up 107 per cent in less than a decade. So they

did - but some of the punch goes out of the magnificent in-

crease when you note the earlier figure includes a much

larger number of partially employed people. If you work

half-time one year and full-time the next, your earnings will

The Well-Chosen Average 35

double, but that doesn't indicate anything at all about your

wage rate.

You may have read in the paper that the income of the

average American family was $6,940 in some specified year.

You should not try to make too much out of that figure

unless you also know what 'family' has been used to mean,

as well as what kind of average this is. (And who says so and

how he knows and how accurate the figure is.)

The figure you saw may have come from the Bureau of

the Census. If you have the Bureau's full report you'll have

no trouble finding right there the rest of the information you

need: that this average is a median; that 'family' signifies

'two or more persons related to each other and living

together'. You will also learn, if you turn back to the tables,

that the figure is based on a sample of such size that there

are nineteen chances out of twenty that the estimate is cor-

rect within a margin of, say, $71 plus or minus.

That probability and that margin add up to a pretty good

estimate. The Census people have both skill enough and

money enough to bring their sampling studies down to a fair

degree of precision. Presumably they have no particular

axes to grind. Not all the figures you see are born under such

happy circumstances, nor are all of them accompanied by

any information at all to show how precise or imprecise

they may be. We'll work that one over in the next chap-

ter.

Meanwhile you may want to try your scepticism on some

items from 'A Letter from the Publisher' in Time magazine.

Of new subscribers it said, Their median age is 34 years and

their average family income is $7,270 a year.' An earlier

survey of 'old TiMErs' had found that their 'median age was

41 years . . . Average income was $9,535 . . .' The natural

question is why, when median is given for ages both times,

the kind of average for incomes is carefully unspecified.

36 How to Lie with Statistics

Could it be that the mean was used instead because it is

bigger, thus seeming to dangle a richer readership before

advertisers?

You might also try a game of what-kind-of-average-are-

you on the alleged prosperity of the 1924 Yales reported at

the beginning of Chapter 1.

Hkfo

n <& tvt uJtTXi®"^**

^"CC

3

The Little

Figures That

Are Not There

What you should do when told the results of a survey, a

statistician once advised, is ask, 'How many juries did you

poll before you found this one?'

As noted previously, well-biased samples can be employed

to produce almost any result anyone may wish. So can

properly random ones, if they are small enough and you

try enough of them.

Users report 23 percent fewer cavities with Doakes' tooth-

paste, the big type says. You could do with twenty-three per

cent fewer aches so you read on. These results, you find,

come from a reassuringly 'independent' laboratory, and the

account is certified by a chartered accountant. What more

do you want?

Yet if you are not outstandingly gullible or optimistic,

you will recall from experience that one toothpaste is

38 How to Lie with Statistics

seldom much better than any other. Then how can the

Doakes people report such results? Can they get away with

telling lies, and in such big type at that? No, and they don't

have to. There are easier ways and more effective ones.

The principal joker in this one is the inadequate sample -

statistically inadequate, that is; for Doakes' purpose it is just

right. That test group of users, you discover by reading the

small type, consisted of just a dozen persons. (You have to

hand it to Doakes, at that, for giving you a sporting chance.

Some advertisers would omit this information and leave

even the statistically sophisticated only a guess as to what

species of chicanery was afoot. His sample of a dozen isn't

so bad either, as these things go. Something called Dr Cor-

nish's Tooth Powder came onto the market a few years ago

with a claim to have shown 'considerable success in cor-

rection of . . . dental caries'. The idea was that the powder

contained urea, which laboratory work was supposed to

have demonstrated to be valuable for the purpose. The

pointlessness of this was that the experimental work had

been purely preliminary and had been done on precisely six

cases.)

Explanation / Answer

Question : Primitive tribe is only five feet, you get a fairly good idea of

the stature of these people. You don't have to ask whether

that average is a mean, median, or mode; it would come out

about the same. (Of course, if you are in the business of

manufacturing overalls for Africans you would want more

information than can be found in any average. This has to

do with ranges and deviations, and we'll tackle that one in

the next chapter.)

Concept: The three most common averages of the mean, median, or mode, can be EASILY used differently at different times, thus making perfectly legal lying possible. The (un)well-chosen average.

A similar concept of changing methods of reporting accounting information, has been used by a lot of corporations to publish lofty profit claims. Enron, for example, changed its revenue recognition principle from agent to dull amount, & reported 70% annual growth over a number of years! It went bankrupt later, of course.

Question : What you should do when told the results of a survey, a

statistician once advised, is ask, 'How many juries did you

poll before you found this one?'

As noted previously, well-biased samples can be employed

to produce almost any result anyone may wish. So can

properly random ones, if they are small enough and you

try enough of them.

Concept :

The concept is of HIDING the unfavorable results that come up and using the law of averages in our favor; if we repeat pretty much ANY experiment a number of times, SOME times a result that we want to show will turn up. We can then, conveniently, ignore the total population space, & ‘prove pretty much any conjecture that is even 0.1% possible, as the dominant outcome.

The little (frequent) figures that are not there.

I hope it was Helpful :)

Related Questions

Navigate

• Browse (All)
• Browse F
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.