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decuslib10-01
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43,50110/statea.dem
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100' NAME--STATEACH
110'
120' DESCRIPTION--TEACH PROGRAM ON COMPUTATION OF BASIC STATISTICS
130'
140' SOURCE--UNKNOWN
150'
160' INSTRUCTIONS--TYPE "LIST" AND FOLLOW INSTRUCTIONS.
170'
180'
190' * * * * * * MAIN PROGRAM * * * * * * * * *
200'
210 NOW THAT YOU UNDERSTAND HOW TO WORK WITH DATA ARRAYED IN
220 MATRICES, CONSIDER SOME OF THE INFORMATION HOU MIGHT LIKE TO KNOW
230 ABOUT THE COLLECTION OF NUMBERS IN A GIVEN ROW OR COLUMN. YOU HAVE
240 ALREADY FOUND THE BIGGEST ELEMENT IN A ROW AND THE AVERAGE OF
250 THE ROW. WHAT ELSE WOULD BE INTERESTING TO KNOW?
260
270
280 ***MEAN, VARIANCE, AND STANDARD DEVIATION***
290
300 ONE OF THE MOST INTERESTING PIECES OF INFORMATION TO KNOW ABOUT
310 A SET OF NUMBERS IS THE STANDARD DEVIATION--A MEASURE OF HOW THE
320 NUMBERS DEVIATE OR SPREAD OUT AROUND THE AVRAGE NUMBER(THE MEAN)
330
340 FOR EXAMPLE, IF THE SET OF DATA IS (3,3,3,3,3) THEN THE MEAN
350 IS 3 AND THE STANDARD DEVIATION IS ZERO BECAUSE THE NUMBERS DON'T
360 DEVIATE AT ALL FROM THE MEAN. THE NUMBERS HAVE NO SPREAD ABOUT THE
370 MEAN. HOWEVER, IF YOUR SET OF DATA IS (1,2,3,4,5) THE STANDARD
380 DEVIATION IS 1.41421 . . . BUT WHAT IS THE STANDARD DEVIATION?
390
400 WELL THE STANDARD DEVIATION IS THE SQUARE ROOT OF THE VARIANCE.
410 BUT WHAT IS THE VARIANCE?
420
430 WELL THE VARIANCE IS SORT OF THE AVERAGE DISTANCE AWAY FROM THE
440 MEAN. WE WILL CONCENTRATE ON FINDING OUT HOW IT IS COMPUTED AND
450 SEE WHAT THE PHRASE "SORT OF AVERAGE DISTANCE" REALLY MEANS.
460
470 TO COMPUTE THE VARIANCE YOU MUST:
480
490 FIRST COMPUTE THE MEAN OF THE DATA.
500
510 SECOND FIND THE DIFFERENCE BETWEEN EACH ELEMENT AND THE
520 MEAN. IF OUR DATA IS (1,2,3,4,5) THEN THE MEAN IS 3 AND
530 THE FIRST DIFFERENCE IS (3-1). BUT NOTICE THE LAST
540 DIFFERENCE IS (3-5). NOW (3-1)=2 BUT (3-5)= -2.
550 WE DON'T REALLY CARE ABOUT THE MINUS SIGN, WE JUST WANT TO
560 KNOW HOW FAR AWAY THE ELEMENT IS. SO WE COULD TAKE THE
570 ABSOLUTE VALUE OF (3-1) AND (3-5). BOTH OF THESE ARE
580 2 . OR WE COULD SIMPLY SQUARE THE VALUE (3-1) AND
590 (3-5)--REMEMBERING THAT ANY NUMBER SQUARED IS POSITIVE--.
600 SO INSTEAD OF GETTING THE DISTANCE AWAY FROM THE MEAN WE
610 GET THE SQUARE OF THE DISTANCE AWAY; IN THE EXAMPLE
620 4 INSTEAD OF 2 .
630 FOR HISTORICAL REASONS THE SQUARE OF THE DISTANCES IS
640 THE MEASURE THAT WE WILL USE IN SPITE OF THE FACT THAT
650 ABSOLUTE VALUE MAY APPEAR MORE NATURAL RIGHT NOW.
660
670 THIRD, WE ADD THE SQUARES OF THE DISTANCE FROM THE MEAN.
680 THAT IS WE SUM THE SQUARE OF THE DIFFERENCES. IN OUR
690 EXAMPLE WE ADD (3-1)^2+(3-2)^2+(3-3)^2+(3-4)^2+(3-5)^2 =
700 4 + 1 + 0 + 1 + 4= 10
710
720 FORTH, WE DIVIDE BY THE NUMBER OF ELEMENTS IN OUR SAMPLE
730 TO GET THE AVERAGE SQUARE DIFFERENCE. IN OUR EXAMPLE
740 WITH FIVE ELEMENTS 10/5 = 2. AND 2 IS THE VARIANCE
750 OF THE SAMPLE.
760
770
780 REMEMBER WE SAID THE SQUARE ROOT OF THE VARIANCE IS THE
790 STANDARD DEVIATION. SO IN OUR EXAMPLE THE STANDARD
800 DEVIATION IS THE SQUARE ROOT OF 2, THAT IS 1.41421 .
810 * * * * * * *
820
830 TRY TO WRITE A PROGRAM THAT READS FIRST N, THE NUMBER OF PIECES
840 OF DATA AND THEN THE DATA AND THEN COMPUTES M, THE MEAN; V, THE
850 VARIANCE AND D, THE STANDARD DEVIATION.
860
870 THERE IS A TEST ROUTINE YOU CAN USE IF YOU LABEL YOUR VARIABLES
880 AS LISTED ABOVE AND IF YOU NAME YOUR PROGRAM STATBGIN .
890 IN OTHER WORDS AFTER YOU HAVE EXPERIMENTED WITH VARIOUS SETS
900 OF DATA, YOU MAY TYPE TEST TO BE SURE YOUR PROGRAM IS CORRECT.
910
920 GOOD LUCK. . . . .