Top: estimated mean L250 as a function of the intrinsic population mean (μ) and standard deviation (σ) of log L250. For each set of (μ, σ), we generate ~2000 random numbers representing the 250 μm luminosities drawn from the log-normal distribution specified by (μ, σ). The estimates of the mean 250 μm luminosity are derived from these specific realisations of log-normal distributions. Bottom: the estimated standard deviation of L250 as a function of μ and σ.