Add some problem solutions

These problems come from Intro to Statistics contest.

Author: derekhh

basic-statistics-warmup-2.cpp

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+#include <iostream>
+#include <iomanip>
+#include <vector>
+#include <numeric>
+#include <algorithm>
+#include <map>
+using namespace std;
+
+vector<int> v;
+map<int, int> m;
+
+int main() {
+  int n;
+  cin >> n;
+  cout.setf(ios::fixed);
+  cout.precision(1);
+  for (int i = 0; i < n; i++) {
+    int num;
+    cin >> num;
+    v.push_back(num);
+  }
+  double mean = accumulate(v.begin(), v.end(), 0) / (double)n;
+  cout << mean << endl;
+  sort(v.begin(), v.end());
+  double median;
+  if (n % 2 == 1)
+    median = v[n / 2];
+  else
+    median = (v[n / 2 - 1] + v[n / 2]) / 2.0;
+  cout << median << endl;
+  for (int i = 0; i < n; i++) {
+    auto it = m.find(v[i]);
+    if (it != m.end())
+      (it->second)++;
+    else
+      m.insert(make_pair(v[i], 1));
+  }
+  int mode, maxTimes = 0;
+  for (auto it = m.begin(); it != m.end(); ++it) {
+    if (it->second > maxTimes || (it->second == maxTimes && it->first < mode)) {
+      mode = it->first;
+      maxTimes = it->second;
+    }
+  }
+  cout << mode << endl;
+  double accum = 0.0;
+  for (int i = 0; i < n; i++) {
+    accum += (v[i] - mean) * (v[i] - mean);
+  }
+  double stdev = sqrt(accum / (double)n);
+  cout << stdev << endl;
+  return 0;
+}

day-5-intro-to-linear-regression.py

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+#day-5-introduction-to-linear-regression.py
+#Day 5: Introduction to Linear Regression
+#Intro to Statistics
+#By derekhh
+#Apr 1, 2016
+
+import numpy as np
+from sklearn import linear_model
+
+x = [95, 85, 80, 70, 60]
+x = np.reshape(x, (5, 1))
+
+y = [85, 95, 70, 65, 70]
+y = np.reshape(y, (5, -1))
+
+reg = linear_model.LinearRegression()
+reg.fit(x, y)
+print("%.1f" % reg.predict([[80]]))

day-5-introduction-to-correlation.py

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+#day-5-introduction-to-correlation.py
+#Day 5: Introduction to Correlation
+#Intro to Statistics
+#By derekhh
+#Apr 1, 2016
+
+from scipy import stats
+
+x = [10, 9.8, 8, 7.8, 7.7, 7, 6, 5, 4, 2]
+y = [200, 44, 32, 24, 22, 17, 15, 12, 8, 4]
+p = stats.pearsonr(x,y)
+r = stats.spearmanr(x, y)
+print("%.3f" % p[0])
+print("%.1f" % r[0])

normal-distribution-1.py

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+#normal-distribution-1.py
+#Normal Distribution #1
+#Intro to Statistics
+#By derekhh
+#Mar 31, 2016
+
+from scipy.stats import norm
+
+distribution = norm(30, 4)
+print("%.3f" % distribution.cdf(40))
+print("%.3f" % (1.0 - distribution.cdf(21)))
+print("%.3f" % (distribution.cdf(35) - (1.0 - distribution.cdf(30))))

normal-distribution-2.py

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+#normal-distribution-2.py
+#Normal Distribution #2
+#Intro to Statistics
+#By derekhh
+#Mar 31, 2016
+
+from scipy.stats import norm
+
+distribution = norm(20, 2)
+print("%.3f" % distribution.cdf(19.5))
+print("%.3f" % (distribution.cdf(22) - (1.0 - distribution.cdf(20))))
+

the-central-limit-theorem-1.py

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+#the-central-limit-theorem-1.py
+#The Central Limit Theorem #1
+#Intro to Statistics
+#By derekhh
+#Mar 31, 2016
+
+from scipy.stats import norm
+
+distribution = norm(205 * 49, 15 * 7)
+print("%.4f" % distribution.cdf(9800))

the-central-limit-theorem-2.py

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+#the-central-limit-theorem-2.py
+#The Central Limit Theorem #2
+#Intro to Statistics
+#By derekhh
+#Mar 31, 2016
+
+from scipy.stats import norm
+
+distribution = norm(2.4 * 100, 2.0 * 10)
+print("%.4f" % distribution.cdf(250))