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Task/Statistics-Basic/Dart/statistics-basic.dart

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+/* Import math library to get:
+ *     	1) Square root function 	        : Math.sqrt(x)
+ *	2) Power function 		: Math.pow(base, exponent)
+ *	3) Random number generator 	: Math.Random()
+ */		
+import 'dart:math' as Math show sqrt, pow, Random;
+
+// Returns average/mean of a list of numbers
+num mean(List<num> l)  => l.reduce((num value,num element)=>value+element)/l.length;
+
+// Returns standard deviation of a list of numbers
+num stdev(List<num> l) => Math.sqrt((1/l.length)*l.map((num x)=>x*x).reduce((num value,num element) => value+element) - Math.pow(mean(l),2));
+
+/* CODE TO PRINT THE HISTOGRAM STARTS HERE
+ *
+ * 	Histogram has ten fields, one for every tenth between 0 and 1
+ * 	To do this, we save the histogram as a global variable
+ * 	that will hold the number of occurences of each tenth in the sample
+ */
+List<num> histogram = new List.filled(10,0);
+
+/*
+ * METHOD TO CREATE A RANDOM SAMPLE OF n NUMBERS (Returns a list)
+ *
+ * 	While creating each value, this method also increments the
+ * 	appropriate index of the histogram
+ */
+List<num> randomsample(num n){
+  List<num> l = new List<num>(n);
+  histogram = new List.filled(10,0);
+  num random = new Math.Random();
+  for (int i = 0; i < n; i++){
+    l[i] = random.nextDouble();
+    histogram[conv(l[i])] += 1;
+  }
+  return l;
+}
+
+/*
+ * METHOD TO RETURN A STRING OF n ASTERIXES (yay ASCII art)
+ */
+String stars(num n){
+  String s = '';
+  for (int i = 0; i < n; i++){
+    s = s + '*';
+  }
+  return s;
+}
+
+/*
+ * METHOD TO DRAW THE HISTOGRAM
+ * 1) Get to total for all the values in the histogram
+ * 2) For every field in the histogram:
+ * 		a) Compute the frequency for every field in the histogram
+ * 		b) Print the frequency as asterixes
+ */
+void drawhistogram(){
+  int total = histogram.reduce((num element,num value)=>element+value);
+  double freq;
+  for (int i = 0; i < 10; i++){
+    freq = histogram[i]/total;
+    print('${i/10} - ${(i+1)/10} : ' + stars(conv(30*freq)));
+  }
+}
+
+/* HELPER METHOD:
+ * 	converts values between 0-1 to integers between 0-9 inclusive
+ * 	useful to figure out which random value generated
+ *	corresponds to which field in the histogram
+ */
+int conv(num i) => (10*i).floor();
+
+
+/* MAIN FUNCTION
+ *
+ * Create 5 histograms and print the mean and standard deviation for each:
+ * 	1) Sample Size = 100
+ *	2) Sample Size = 1000
+ *	3) Sample Size = 10000
+ *	4) Sample Size = 100000
+ *	5) Sample Size = 1000000
+ *
+ */
+void main(){
+  List<num> l;
+  num m;
+  num s;
+  List<int> sampleSizes = [100,1000,10000,100000,1000000];
+  for (int samplesize in sampleSizes){
+    print('---------------  Sample size $samplesize   ----------------');
+    l = randomsample(samplesize);
+    m = mean(l);
+    s = stdev(l);
+    drawhistogram();
+    print('');
+    print('mean: ${m.toStringAsPrecision(8)}   standard deviation: ${s.toStringAsPrecision(8)}');
+    print('');
+  }
+}