How to get the mean and std. of bits (fragments) of data?

I'm not super certain of what you're asking for... below is a snippet that will return a 2D free wave with the average and standard deviation of each contiguous chunk of data only; so, e.g.if there are two contiguous chunks like shown in your image, then the result will be a 2x2 matrix. There may be more efficient ways to do this, and you may not want just the values if you have timeseries data for example.

//___________________________________________________________________________________________________
// Get average and standard deviation of each chunk of data.
Function/WAVE StatsNonNaNs(Wave inWv)	

	int i,k,q,n=numpnts(inWv)
	Make /FREE /N=(0,2) outWv = NaN
		
	do
		if (numtype(inWv[i]) == 0)
			k=i						
			do							
				k++
			while ( (k < i) && (k < n) )
			q=k-1
			if (numtype(inWv[k]) == 0)   	
				do							
					k++
					if (k == n)
						break	
					endif
				while ((numtype(inWv[k]) == 0) && (k < n)) 
				k--						
				if ((k-q)  >= 1)		
					InsertPoints /M=0 Inf, 1, outWv
					WaveStats/Q/R=[q, k]/M=2 inWv
					outWv[Inf][0] = V_avg
					outWv[Inf][1] = V_sdev
				endif
				i=k
			else		
				i=k
			endif	
		else
			i++
		endif
	while (i < n-1)	
	
	return outWv
end
//___________________________________________________________________________________________________