On 2012-01-23 19:10:28 +0000, Ray Fischer said:

> Eric Stevens <(E-Mail Removed)> wrote:

>> On 23 Jan 2012 07:29:07 GMT, (E-Mail Removed) (Ray Fischer) wrote:

>>

>>> Eric Stevens <(E-Mail Removed)> wrote:

>>>> On 22 Jan 2012 23:13:43 GMT, (E-Mail Removed) (Ray Fischer) wrote:

>>>>

>>>>> PeterN <(E-Mail Removed)> wrote:

>>>>>> On 1/22/2012 4:06 PM, Ray Fischer wrote:

>>>>>>> PeterN<(E-Mail Removed)> wrote:

>>>>>>>> On 1/22/2012 12:03 PM, Alan Browne wrote:

>>>>>>>>> On 2012-01-22 11:26 , tony cooper wrote:

>>>>>>>>>> "Impossible" was not a word chosen wisely. In this area, there are

>>>>>>>>>> magnet schools for the gifted. I would imagine that all of the

>>>>>>>>>> students in a school such as this would be above-average in

>>>>>>>>>> intelligence for their age group.

>>>>>>>>>

>>>>>>>>> Correct. However the context of the statement (that Pete supplied) is in

>>>>>>>>> the general school system.

>>>>>>>>>

>>>>>>>>> Quibble: it's not about 'intelligence' but performance and test results.

>>>>>>>>

>>>>>>>> My quibble:

>>>>>>>>

>>>>>>>> Assume a student population of 100.

>>>>>>>> The grade points are;

>>>>>>>> 75 A

>>>>>>>> 25 c

>>>>>>>>

>>>>>>>> Obviously more than half the students will be above average.

>>>>>>>

>>>>>>> Nope. The average is an A. No students are above average and

>>>>>>> many are below average.

>>>>>>>

>>>>>>> The math:

>>>>>>> A = 4

>>>>>>> C = 2

>>>>>>> (75 * 4) + (25 * 2) = 350

>>>>>>> 350 / 100 = 3.5 = A (rounded to the nearest letter grade)

>>>>>>

>>>>>> You didn't account for compensation for skewed curves.

>>>>>

>>>>> I was pointing out the fallacy of depending on rounded values.

>>>>> By definition, you cannot have more than half of the students

>>>>> score above average.

>>>>

>>>> Umm - you can you know.

>>>>

>>>> 52 52 52 53 53 55 59 52 52 25

>>>>

>>>> 10 students with an average of 45.

>>>

>>> Your calculator is broken.

>>

>> I realised that was wrong after I posted.

>

> In more than one way.

>

>> I'm the last one with 25. Knock off 5 marks for my mistake and the

>

> You playing games by depending on rounding errors and too-small sample

> sizes.
It's a completely valid dataset. It is the analysis of it that has lead

to the false claim that it proves more than half of the students score

above average.

The "average" value of a dataset is a single number that most typifies

the datapoints within it. Here's the dataset placed in order:

25 52 52 52 52 52 53 53 53 59

We can see by inspection that a suitable average is 52 or 53. Three

commonly-used methods of calculating the average are:

mean: 50.5

median: 52

mode: 52

The arithmetic mean (aka mean) has been influenced heavily by the

outlying datapoint of 25. An extreme example is:

100000 52 52 52 52 52 53 53 53 59

mean: 10048

median: 52.5

mode: 52

This time, it's completely obvious that the mean of 10048 does _not_

typify the values in the dataset

The median is a far better average for data with high varience because

it not only better typifies the dataset, it also prevents absurd

conclusions being drawn such as "all but one of the values is far below

average". The median is calculated such that no more than half of the

samples can be above average and no more than half can be below.

In the original dataset, with a median of 52, one data point is below

average, 4 are average, and 4 are above average.

In the second example, with a median of 52.5, half of the dataset is

below average, the other half is above.

The term "average" is often thought to imply only the arithmetic mean,

but this is a misnomer.