# 11.5. Computing Variance, Standard Deviation, and Other Statistical Functions

## Problem

You want to compute one or more of the common statistics such as variance, standard deviation, skew, and kurtosis of a sequence of numbers.

## Solution

You can use the `accumulate` function from the `<numeric>` header to compute many meaningful statistical functions beyond simply the sum by passing custom function objects. Example 11-9 shows how to compute several important statistical functions, using `accumulate`.

Example 11-9. Statistical functions

`#include <numeric> #include <cmath> #include <algorithm> #include <functional> #include <vector> #include <iostream> using namespace std; template<int N, class T> T nthPower(T x) { T ret = x; for (int i=1; i < N; ++i) { ret *= x; } return ret; } template<class T, int N> struct SumDiffNthPower { SumDiffNthPower(T x) : mean_(x) { }; T operator()(T sum, T current) { return sum + nthPower<N>(current - mean_); } T mean_; }; template<class T, int N, class Iter_T> T nthMoment(Iter_T first, Iter_T last, T mean) { size_t cnt = distance(first, last); return accumulate(first, last, T(), SumDiffNthPower<T, N>(mean)) / cnt; } template<class T, class Iter_T> T computeVariance(Iter_T first, Iter_T last, T mean) { return nthMoment<T, 2>(first, last, mean); } template<class T, class Iter_T> T computeStdDev(Iter_T first, Iter_T last, T mean) { return sqrt(computeVariance(first, last, mean)); } template<class T, class Iter_T> T computeSkew(Iter_T begin, Iter_T end, T mean) ...`

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