<SYSTEM_TASK:>
Solve the following problem using Python, implementing the functions described below, one line at a time
<END_TASK>
<USER_TASK:>
Description:
 def _sd_of_runs(stats, mean, key='runs'):
 """Obtain the standard deviation of stats. Args: stats: dict; A set of stats, structured as above. mean: dict; Mean for each key in stats. key: str; Optional key to determine where list of runs is found in stats """


    num_runs = len(stats[key])
    first = stats[key][0]

    standard_deviation = {}
    for stat_key in first:
        # Skip non numberic attributes
        if isinstance(first[stat_key], numbers.Number):
            standard_deviation[stat_key] = math.sqrt(
                sum((run[stat_key] - mean[stat_key])**2
                    for run in stats[key]) / float(num_runs))

    return standard_deviation