Condensate clouds strongly impact the spectra of brown dwarfs and exoplanets .
Recent discoveries of variable L/T transition dwarfs argued for patchy clouds in at least some ultracool atmospheres .
This study aims to measure the frequency and level of spectral variability in brown dwarfs and to search for correlations with spectral type .
We used HST/WFC3 to obtain spectroscopic time series for 22 brown dwarfs of spectral types ranging from L5 to T6 at 1.1-1.7Â \mu m for \approx 40Â min per object .
Using Bayesian analysis , we find 6 brown dwarfs with confident ( p > 95 \% ) variability in the relative flux in at least one wavelength region at sub-percent precision , and 5 brown dwarfs with tentative ( p > 68 \% ) variability .
We derive a minimum variability fraction f _ { min } = 27 ^ { +11 } _ { -7 } \% over all covered spectral types .
The fraction of variables is equal within errors for mid L , late L and mid T spectral types ; for early T dwarfs we do not find any confident variable but the sample is too small to derive meaningful limits .
For some objects , the variability occurs primarily in the flux peak in the J or H band , others are variable throughout the spectrum or only in specific absorption regions .
Four sources may have broad-band peak-to-peak amplitudes exceeding 1 % .
Our measurements are not sensitive to very long periods , inclinations near pole-on and rotationally symmetric heterogeneity .
The detection statistics are consistent with most brown dwarf photospheres being patchy .
While multiple-percent near-infrared variability may be rare and confined to the L/T transition , low-level heterogeneities are a frequent characteristic of brown dwarf atmospheres .