The validity of assuming that a simple, low-dimensional manifold can su ciently accurately represent the chemical state in a turbulent ame is investigated. The experimental data from the Cambridge/Sandia strati ed swirl burner working in nine di erent con gurations are post- processed to explore the e ects of coordinate, swirl ow ratio, and strati cation factor on the conditionally-averaged reactive scalars. First, the mixture fraction and thermal progress variable are employed to construct a two-dimensional conditional manifold by using all of the data { regardless of the coordinate in the physical domain, swirl ratio, and strati cation factor. Moreover, one-point, one-time measurements are utilized to compute the exact joint Probabil- ity Density Function (PDF) of the conditioning variables at each point. Having the conditional averages of temperature and mass fractions of CO2, CO, CH4, H2, and H2O in addition to the joint PDF of the conditioning variables, the low-dimensional manifold is applied to cal- culate the unconditional averages for each of the scalars. The mean values are also obtained by ensemble averaging all of the data available for each of the measuring points, and the dis- crepancies between the values calculated from the two approaches are reported in order to assess the validity of the assumptions underlying the low-dimensional chemistry representa- tions. The results suggest that the two chosen conditioning variables are not su cient to make the manifold independent of the real domain, so, the normalized total enthalpy is introduced as the third conditioning variable and the process repeated. Results obtained from the three- condition manifold demonstrate that the discrepancies for prediction of the reactive scalars, more signi cantly for CO2 and CO mass fractions, decrease when using the third condition. The discrepancies with three conditions show that a three-dimensional manifold is su cient to assume the conditional averages are independent of swirl and strati cation. A normalized accumulated discrepancy is used as a metric for each of the cases so one can see the overall e ect of each assumption that is made for constructing the conditional manifold. Decoupling the manifold from the coordinate, swirl ratio, and strati cation level makes it possible to ob- tain the ltered chemical source-terms from a static lookup table for many ames which will considerably reduce the computational cost for simulating turbulent reacting ows.