Does a low-volume day on MNQ tend to precede a large range day

et = to_et(bars)
rth = rth_session(et)
rth = rth.copy()
rth['date'] = trading_date(rth)

daily = rth.groupby('date').agg(
    high=('high','max'),
    low=('low','min'),
    volume=('volume','sum')
)
daily['range'] = daily['high'] - daily['low']
daily = daily.dropna()
daily = daily.sort_index()

# shift volume to previous day, align with next day's range
daily['prev_volume'] = daily['volume'].shift(1)
daily['prev_range'] = daily['range'].shift(1)

valid = daily.dropna(subset=['prev_volume','range'])

if len(valid) >= 5:
    low_vol_thresh = valid['prev_volume'].quantile(0.3)
    high_range_thresh = valid['range'].quantile(0.7)

    low_vol_days = valid[valid['prev_volume'] <= low_vol_thresh]
    other_days = valid[valid['prev_volume'] > low_vol_thresh]

    low_vol_next_range_mean = float(low_vol_days['range'].mean())
    other_next_range_mean = float(other_days['range'].mean()) if len(other_days) > 0 else None

    low_vol_large_range_rate = float((low_vol_days['range'] >= high_range_thresh).mean())
    other_large_range_rate = float((other_days['range'] >= high_range_thresh).mean()) if len(other_days) > 0 else None

    corr = float(valid['prev_volume'].corr(valid['range']))

    result = {
        'sample_size': int(len(valid)),
        'n_low_volume_days': int(len(low_vol_days)),
        'n_other_days': int(len(other_days)),
        'low_vol_threshold': float(low_vol_thresh),
        'high_range_threshold': float(high_range_thresh),
        'avg_range_after_low_volume': low_vol_next_range_mean,
        'avg_range_after_other': other_next_range_mean,
        'large_range_rate_after_low_volume': low_vol_large_range_rate,
        'large_range_rate_after_other': other_large_range_rate,
        'correlation_prevvol_range': corr,
    }
else:
    result = {
        'sample_size': int(len(valid)),
        'n_low_volume_days': 0,
        'n_other_days': 0,
        'low_vol_threshold': None,
        'high_range_threshold': None,
        'avg_range_after_low_volume': None,
        'avg_range_after_other': None,
        'large_range_rate_after_low_volume': None,
        'large_range_rate_after_other': None,
        'correlation_prevvol_range': None,
    }