I figure unless your meter has a "Peak" function (not MIN/MAX) - it is integrating/averaging the level over a short period of time.
Typical is A/C weighting, slow and fast integration, MIN/MAX hold.
MIN/MAX displays the lowest/highest averaged levels, not Peak.
I have a UMIK-1 and REW - the integrating measurements there match my cheap averaging handheld meter, the peak readings make sense in the context of my measurements.
Example:
Unweighted (no filter), C weighted, and A weighted measurements of room background and a single hand-clap at about 5 feet off to the side.
Numbers on the left are fast averaged and weighted min and max, and unweighted peak.
From REW Help File:
The meter displays either sound pressure level (SPL), time-average equivalent sound level (Leq) or sound exposure level (LE) according to the selection made on the buttons below the display. The SPL reading is filtered with either a "Fast" (125ms) or "Slow" (1s) time constant, selected via the F/S buttons.
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My normal-efficient panels (about 88dB @ 2.83v at the listening position) showed no onset of compression on sweeps up to 95dB or so (which is not saying a lot, but that's what I looked at).
They have produced 116.9dB on some drumming peaks at the listening position, which was so loud as to border on the ridiculous/dangerous, so I don't do that. It was a brief calibrated experiment.
110dB peaks is about the loudest occasional "normal" Beer Saturday Night peak loud I get here, 105dB commonly seen loud, 100db normal listening loud.
Right now,
Charlie Hunter Trio, but from CD:
Here's an informative glossary about Sound Levels:
http://www.acoustic-glossary.co.uk/