dashed lines show the quiescent fractions in projection radius with spectral-$z$ and photo-$z$, respectively. Additionally, three solid lines represent the best-fitting results for the three different cases stated above. The projected $f_q$ for photo-$z$ galaxies agrees very well with that for spectral-$z$ galaxies, suggesting that the photo-$z$ uncertainty has little effect on the resulting $f_q$. If the background subtraction’ can properly remove background galaxies, the projected $f_q$ in groups or in clusters can be well recovered.[]{data-label="f3"}](f3.eps)

![image](f4.eps)

![ Top: the quiescent fraction $f_q$ as a function of the stellar mass $M_*$. The purple pluses and blue stars denote the $f_q$ in redshift range of 0.2 $< z <$ 0.5 and 0.5 $< z <$ 0.8, respectively. For comparisons, the $f_q$s from [@wag17] in 0.15 $<  z <$ 0.41 (green squares) and 0.41 $<  z <$ 0.80 (yellow squares) are included. Bottom: The SSFR of star-forming cluster (solid lines) and field (dashed lines) galaxies as a function of the stellar mass $M_*$ in 0.2 $< z <$ 0.5 (purple pluses) and 0.5 $< z <$ 0.8 (blue stars). The green squares show the SSFRs of star-forming cluster galaxies in 0.15 $< z <$ 0.8 from [@wag17].[]{data-label="f5"}](f5.eps)

Method and Tests
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Background 