Slightly stylized:

template <typename It, typename E = typename std::iterator_traits<It>::value_type>
E std_dev(It b, It e)
{
    E N          = std::distance(b, e);
    E const mean = std::accumulate(b, e, E{}) / N;
    E variance   = std::accumulate(b, e, E{}, [mean](E a, E v)-> E { return a + (v-mean)*(v-mean); });
    return std::sqrt(variance / N);
}

Slightly stylized, with comparison to Boost Accumulator:

Live On Coliru

#include <iostream>
#include <iterator>
#include <vector>
#include <algorithm>

#include <boost/accumulators/accumulators.hpp>
#include <boost/accumulators/statistics.hpp>

template <typename It, typename E = typename std::iterator_traits<It>::value_type, typename R = typename std::common_type<double, E>::type>
R std_dev_boost(It begin, It end){
    namespace ba = boost::accumulators;

    ba::accumulator_set<R, ba::stats<ba::tag::variance> > accu;
    std::for_each(begin, end, std::ref(accu));
    return std::sqrt(ba::variance(accu));
}

template <typename It, 
    typename E = typename std::iterator_traits<It>::value_type, 
    typename R = typename std::common_type<double, E>::type>
R std_dev(It b, It e)
{
    R N          = std::distance(b, e);
    R const mean = std::accumulate(b, e, R{}) / N;
    R variance   = std::accumulate(b, e, R{}, [mean](R a, E v)-> R { return a + (v-mean)*(v-mean); });
    return std::sqrt(variance / N);
}

int main(){
    std::vector<int> stuff {35, 34, 36, 39, 35, 35, 35, 35, 35};
    std::cout << std_dev_boost(stuff.begin(), stuff.end()) << "\n";
    std::cout << std_dev      (stuff.begin(), stuff.end()) << "\n";
}

Prints

1.34256
1.34256

Firstly, make it correct.

N is integral, so you get truncation errors.

N-1 is wrong.

Rename average to mean.

Don't hardcode E.

You get:

template <typename It, typename E = typename std::iterator_traits<It>::value_type>
E std_dev(It begin, It end){
    E N = std::distance(begin, end);
    E const mean = std::accumulate(begin, end, E()) / N;
    auto sum_term = [mean](E init, E value)-> E { return init + (value - mean)*(value - mean); };
    E variance = std::accumulate(begin, end, E(), sum_term);
    return std::sqrt(variance / N);
}

Firstly, make it correct.

N is integral, you could make it E so you don't accidentally do integer arithmetic.

N-1 is wrong.

Rename average to mean.

Don't hardcode E.

You get:

template <typename It, typename E = typename std::iterator_traits<It>::value_type>
E std_dev(It begin, It end){
    E N = std::distance(begin, end);
    E const mean = std::accumulate(begin, end, E()) / N;
    auto sum_term = [mean](E init, E value)-> E { return init + (value - mean)*(value - mean); };
    E variance = std::accumulate(begin, end, E(), sum_term);
    return std::sqrt(variance / N);
}

Slightly stylized:

template <typename It, typename E = typename std::iterator_traits<It>::value_type>
E std_dev(It b, It e)
{
    E N          = std::distance(b, e);
    E const mean = std::accumulate(b, e, E{}) / N;
    E variance   = std::accumulate(b, e, E{}, [mean](E a, E v)-> E { return a + (v-mean)*(v-mean); });
    return std::sqrt(variance / N);
}