Data update

Task/Statistics-Normal-distribution/QBasic/statistics-normal-distribution.basic

@@ -0,0 +1,92 @@
+DECLARE FUNCTION randomNormal! ()
+DECLARE SUB normalStats (sampleSize)
+
+CONST pi = 3.141592653589793#
+RANDOMIZE TIMER
+
+CLS
+CALL normalStats(100)
+PRINT
+CALL normalStats(1000)
+PRINT
+CALL normalStats(10000)
+PRINT
+CALL normalStats(100000)
+PRINT "Press any key to quit"
+END
+
+SUB normalStats (sampleSize)
+    IF sampleSize < 1 THEN EXIT SUB
+
+    DIM r(1 TO sampleSize) AS SINGLE
+    DIM h(-1 TO 10) AS INTEGER
+    DIM sum AS DOUBLE: sum = 0!
+    DIM hSum AS INTEGER: hSum = 0
+    DIM i AS INTEGER
+
+    ' Generate samples: mean 0.5, std 0.25
+    FOR i = 1 TO sampleSize
+        r(i) = .5 + randomNormal! / 4!
+        sum = sum + r(i)
+
+        IF r(i) < 0! THEN
+            h(-1) = h(-1) + 1
+        ELSEIF r(i) >= 1! THEN
+            h(10) = h(10) + 1
+        ELSE
+            h(INT(r(i) * 10)) = h(INT(r(i) * 10)) + 1
+        END IF
+    NEXT i
+
+    FOR i = -1 TO 10
+        hSum = hSum + h(i)
+    NEXT i
+
+    ' Adjust if necessary (rounding error)
+    DIM adj AS INTEGER: adj = sampleSize - hSum
+    IF adj <> 0 THEN
+        FOR i = -1 TO 10
+            h(i) = h(i) + adj
+            IF h(i) >= 0 THEN EXIT FOR
+            h(i) = h(i) - adj
+        NEXT i
+    END IF
+
+    DIM mean AS DOUBLE: mean = sum / sampleSize
+
+    ' Standard deviation
+    sum = 0!
+    FOR i = 1 TO sampleSize
+        sum = sum + (r(i) - mean) ^ 2!
+    NEXT i
+    DIM sd AS DOUBLE: sd = SQR(sum / sampleSize)
+
+    PRINT "Sample size"; sampleSize
+    PRINT
+    PRINT USING "  Mean #.######"; mean;
+    PRINT USING "  SD #.######"; sd
+    PRINT
+
+    ' Histogram (scale large samples)
+    DIM numStars AS INTEGER
+    DIM scale AS DOUBLE: scale = 1!
+    IF sampleSize > 300 THEN scale = 300 / sampleSize
+
+    FOR i = -1 TO 10
+        IF i = -1 THEN
+            PRINT "< 0.00  : ";
+        ELSEIF i = 10 THEN
+            PRINT ">=1.00  : ";
+        ELSE
+            PRINT USING "  #.##  : "; i / 10;
+        END IF
+
+        PRINT USING "##### "; h(i);
+        numStars = INT(h(i) * scale + .5)
+        PRINT STRING$(numStars, "*")
+    NEXT i
+END SUB
+
+FUNCTION randomNormal!
+    randomNormal! = COS(2 * pi * RND) * SQR(-2 * LOG(RND))
+END FUNCTION