About statistics

The use of statistics is quite a game, Boss, and i would advise not putting a lot of credence in them. When someone cites a statistic, you don't, for example, know what has been left out of the calculation. Quite apart from not knowing the reliability of the person citing the statistic, all sorts of other questions crop up. In polls, it is useful to know how large the sample is, how the respondants were chosen, how the question was framed, the means of polling (people, for example, seem to answer differently when asked in person than when polled by telephone).

In the statistics released by agencies, it is important to know just exactly the demographic of the population an agency serves. Regions matter as well, both in polls and agency statistics. One of the most famous, and flagrant abuses of statistics took place during the time when Reagan was President of the United States. Reagan slashed taxes and gutted federal regulatory agencies. The response of investors in the United States was a feeding frenzy, and the Wall Street index jumped to historic new highs. Unemployment dramatically rose, as well. So the administration began counting active duty members of the armed forces among the employed, which effectively "lowered" the percentage of employment. You would always do well to be cautious with statistics, and to use them only as sign posts to find your way through the details of any issue.

thanks

well, for an expample:
There is a group with 30 persons , 13 persons with the age 18 ,
7 are 17
and 10 are 16

so which is the average age?

I don´t understand this till now

for that, it is quite simple, you multiply each age by the number of persons of that age, and then divide the product by 30, the number in the sample . . . you are actually asking about the mathmatically bases of statisticaly analysis . . .

Edit: had i paid more attention, i'd have realized that in this category, that is the nature of your question by inference . . . doh ! ! !

I know, I want to get on this mathematically topic.

So thanks very large

Maybe other questions upcoming....

Mark Twain said "There are lies, there are damned lies, and then there are statistics". A bit harsh, perhaps, but not entirely inaccurate. Often, "Statistics" effectively are little more than a complilation of data selected, arranged, and presented in such manner as to support or refute a given proposition.


A generally accepted academic definition of Statistics is "An aggregate of facts affected to a given, stated, extent by multiplicity of causes, numerically expressed, enumerated or estimated according to a given, stated standard of accuracy, collected in a systematic manner for a predetermined purpose and placed in relation to each other." Another would be "The collection, presentation, analysis and interpretation of a given srt of numerical data."

"Deductive Statistics" entails the collection of selected ob servations, data, either qualitative or quntitative, relating to a given sample group or population (often termed "The Sample Universe", as for the purposes of the analysis at hand, nothing beyond or apart from the selected group or population exists as consideration) in order to draw inferences about the selected Sample Universe. Another term for this branch of statistics is "Descriptive Statistics". "Inferential Staistics", or "Inductive Statistics" entails applying statistical analysis to draw inferences about the "Universe" beyond the "Sample Universe". Among other subsets of statitics are "Predictive Statistics", which purport to quantify the probability of future condition by means of analysis of data observed of past phenomona. The quantity and quality of the data selected, and the academic integrety of the analysis applied, define the validity of any statistical analysis; "Garbage In = Garbage Out"

In short, "Statistics" is a buncha numbers. "Statistical Analysis" is what is done with those numbers ... and just about anything desired can be done with just about any set of numbers by means of structuring the selection of and the analysis applied to those numbers.

Re: About statistics

There is probably a good Schaum's outline or something like that which would explain the basics.

Thok, what you must never forget is that 76% of statistical facts are based on b*******, the other 58% are just someones way of trying to make the hoi polloi vote the way that suits their hidden agenda.

Thok, Don't get turned off by the negative comments about statistics. Sure, statistics can be misused, but the same can be said for other fields. Garbage in, garbage out.

The public should be wary of the "average" There are three basic "averages"
MEAN AVERAGE. Add all the items and divide by the number of items.
MEDIAN AVERAGE. You use the middle number
MODE AVERAGE. The most common or typical figure.

Say you want to find the average household income in a village of ten households.

$24,000
$24,000
$25,000
$25,000
$25,000
$30,000
$30,000
$30,000
$30,000`
$1,000,000

So we total them 1,243,000
and divide by 10 to get $1,243,000.

So, based on a MEAN AVERAGE, the average household in our mythical little village brings in $124,300. That's based on a MEAN AVERAGE.

The MEDIAN AVERAGE is the middle figure or
$25,000.

And the MODE AVERAGE is the most common number which is $30,000.

Which "average" seems right to you?

Confidence intervals are also big in statistics. That is where you say, "The probability is 95% that the mean of the population, or the standard deviation of the population (etc.) lies between these two numbers."

Then, there are the statistical distributions like the Normal, Poisson, Binomial, Exponential, etc. The Normal distribution is very important because of something called the Central Limit Theorem.

Statistics is very useful to scientists for interpreting experimental results.

I had to take enough of this in school that I became very impressed by the potential of the field.

There are two sorts of statistics; Deductive and Inferential. Deductive Statistics mostly describe an existing set, and Inferential Statistics use mathematics to infer, or identify and project trends or tendencies into the future. Here we will just talk about Deductive and averages.

There are three sorts of averages: Mean, Mode and Median.

Mean is the sum of the scores divided by the number of scores. 4+2+8=14/3= a mean of 4.667 (at or above .5 round up, below .5 round down)

Median is the midpoint between largest and smallest scores (Range) in the set. In the case of 4, 2, 8 the median is 6 (8-4=4 4/2=2 2+4=6).

Mode is the score in the set where most cases occur. In sets as small as the example used so far, the Mode doesn't mean very much. However, in large sets the mode if often what people mean when the say that something is "average". For instance when a newspaper says that the average annual family income is $34,000 they are talking about the Mode. In moderate size sets statisticians usually group scores into cohorts. A cohort is a sub-set that groups things. For instance we might group ages Birth to age 10, age 10 to 20, age 20 to 30, and so forth. This is one means of "smoothing" with large numbers in forms where we can work with them. Modes are very useful, especially when the results are graphically regarded.

The scores are placed onto a chart with X and Y axis, the result in a perfectly random sample will be a bell shaped curve that is more, or less, symmetrical. The smallest numbers appear at the extremes, with the largest number in the center. In a class of 100 students a few will have poor grades and a few will have very good grades, but most will fall somewhere in between. That in between is the Mode. By calculating the standard deviation of scores one can begin to understand just how much any score varies from the central tendency. If for instance in our class of 100 students 1 grade was 75, 35 were 76-80, and 24 were between 81 and 90,and 2 were above 91, we can see that the scores are skewed pretty much toward the low end of the bell curve. We would expect the scores in this example for most cases to cluster around the Mode of 82. That sort of result causes us to question, why is the curve skewed?

One of the reasons that we use statistics is that it often is impractical to use ever score within a set, especially when dealing with very large sets. For instance it would be difficult to get the income of every person within the United States, so a representative sample is taken. How large a sample is necessary to properly represent a set as large as the population of a large country? Though you might think the sample is very large, mathematically the number is really quite reasonable. if an old man's memory serves, a truly random and representative sample of something like 36 is adequate to representl almost any set. Never-the-less statistical polls usually try to randomly capture thousands of scores before attempting analysis. Why is random sampling so important. Think of how skewed the result might be if in trying to determine the "average" income of Americans you only sampled people living in Beverly Hills, or in East Gopher Village, Oklahoma. As you can readily see sample size and selection are both very important.

I hope that this will help make statistics easier for you to understand, and use.

Thanks Ashermam for explaining "averages" to Thok better than I could. That's not in my expertise.
I jsut know enough to be wary of the word "average"

Actually, median is the value in the set in which the number of greater values is equal to the number of lesser values. This is very different than the midpoint between the two greatest and least value.

Example:

The median of {1,2,3,3,4,4,4,5,5} is 4. The midpoint between the outliers is 3.