We investigate the relation between trading activity - measured by the number of trades [iopmath latex="$N_Delta t$"] N_t [/iopmath] - and the price change [iopmath latex="$G_Delta t$"] G_t [/iopmath] for a given stock over a time interval [iopmath latex="$[t,~t+Delta t]$"] [t, t + t] [/iopmath] . We relate the time-dependent standard deviation of price changes - volatility - to two microscopic quantities: the number of transactions [iopmath latex="$N_Delta t$"] N_t [/iopmath] in [iopmath latex="$Delta t$"] t [/iopmath] and the variance [iopmath latex="$W^2_Delta t$"] W²_t [/iopmath] of the price changes for all transactions in [iopmath latex="$Delta t$"] t [/iopmath] . We find that [iopmath latex="$N_Delta t$"] N_t [/iopmath] displays power-law decaying time correlations whereas [iopmath latex="$W_Delta t$"] W_t [/iopmath] displays only weak time correlations, indicating that the long-range correlations previously found in [iopmath latex="$vert G_Delta t vert$"] |G_t| [/iopmath] are largely due to those of [iopmath latex="$N_Delta t$"] N_t [/iopmath] . Further, we analyse the distribution [iopmath latex="$PN_Delta t gt x$"] PN_t>x [/iopmath] and find an asymptotic behaviour consistent with a power-law decay. We then argue that the tail-exponent of [iopmath latex="$PN_Delta t gt x$"] PN_t>x [/iopmath] is insufficient to account for the tail-exponent of [iopmath latex="$PG_Delta t gt x$"] PG_t>x [/iopmath] . Since [iopmath latex="$N_Delta t$"] N_t [/iopmath] and [iopmath latex="$W_Delta t$"] W_t [/iopmath] display only weak interdependence, we argue that the fat tails of the distribution [iopmath latex="$PG_Delta t gt x$"] PG_t>x [/iopmath] arise from [iopmath latex="$W_Delta t$"] W_t [/iopmath] , which has a distribution with power-law tail exponent consistent with our estimates for [iopmath latex="$G_Delta t$"] G_t [/iopmath] . Further, we analyse the statistical properties of the number of shares [iopmath latex="$Q_Delta t$"] Q_t [/iopmath] traded in [iopmath latex="$Delta t$"] t [/iopmath] , and find that the distribution of [iopmath latex="$Q_Delta t$"] Q_t [/iopmath] is consistent with a Lvy-stable distribution. We also quantify the relationship between [iopmath latex="$Q_Delta t$"] Q_t [/iopmath] and [iopmath latex="$N_Delta t$"] N_t [/iopmath] , which provides one explanation for the previously observed volume-volatility co-movement.