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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);
}