Calculation of Seasonal Variation

A financial analyst is examining the quarterly sales data of a retail store, measured in thousands of dollars. The analyst observes that the sales data exhibits a recurring pattern over the four quarters of each year, peaking in the fourth quarter during the holiday season, and dropping to a trough in the first quarter following the winter holidays.

The analyst applies a seasonal decomposition method to quantify the effect of seasonality on the sales data. If the analyst uses the additive model for decomposition, the model can be represented as:

$$ Y_t = T_t + S_t + E_t $$

Where:
$Y_t$ = the observed data at time $t$
$T_t$ = the trend component
$S_t$ = the seasonal component
$E_t$ = the error component

Given that the annual sales figures totaled $1,200,000 in a given year, and the analysis indicates that the seasonal component ($S_t$) contributes an increase of $50,000 in Q4 and a decrease of $30,000 in Q1, what is the reported seasonal variation for the retail store?