IMO it doesn't show that, rather it shows a pretty typical, perhaps even average utilisation of 2.4GHz, but not high.
It is a common misunderstanding, interference index in the context of ARM commands is not "rf interference" rather it is "presence of other APs".
You can consider the "noise" (floor) value to be one indidcator (see note1 below) of non 802.11 "rf interference", in which case you could say ch. 6 is slightly impaired with a value of 82.
The other number you should consider is the ch. utilisation, values in the 80s or higher would be a problem, in this capture they are more or less what might be exected for a dense 2.4GHz network.
Interference index values in the 100s look unappealing but not the sole metric for seeing whether your channel(s) are impaired enough to degrade the user experience. As desribed above, the inteference index just means APs are present, the ch. utilisation is a more interesting number.
If you are running a lot of APs, and this output is typical of your APs, it may be indicative that you have 2.4GHz tx power set a bit high (as indicated by the relatively high coverage index values shown)
To the other half of the question - airwave. Yes, Airwave will show you utilisation (which includes interference, see note1) and noise floor over time. Go into the AP within Airwave, click the radio, choose channel utilisation from the drop down and then click once on the chart to pop it out so you can pinch and zoom etc. Attached some images that show this in case you're not familiar.
Note 1: The value of "interference" being plotted by Airwave is different again than the "interference index". In this case, interference is the delta of the channel busy, rx busy and tx busy, or said another way
Interference = ch busy - rx busy - tx busy
this difference value is plotted by airwave (the IAP CLI commands don't show it explicity I believe, but controller based APs show it in show ap radio-summary). You can also just calculate it visually from the rf summary, e.g.
1 0 0 0 96 27/21/3/0/97 27 - 21 - 3 == 3
6 0 0 0 82 54/40/5/0/70 54 - 40 - 5 == 9
11 0 0 0 91 29/23/2/0/67 29 - 23 - 2 == 4
are these values bad ? not really. For 2.4GHz, seeing values of I into the 20s would be high, but there is generally not a lot you can do about it. A value of 9 is getting up there, likely related to the high-ish noise vaue of 82, worth looking at how it behaves over time (from airwave).
All in all, things look within expectation for 2.4GHz, maybe check your max tx power settings for 2.4GHz though, and dig a bit more into the noise on ch 6 versus time of day and user load.
hth.