Calculate black shirts for Q

Ratio of Black to White is $9:5$, sum of parts $= 9+5 = 14$. Black shirts in Q $= (9/14) \times 3150 = 9 \times 225$.

$9 \times 225 = 2025$

Calculate black shirts for R

Ratio of Black to White is $7:8$, sum of parts $= 7+8 = 15$. Black shirts in R $= (7/15) \times 5625 = 7 \times 375$.

$7 \times 375 = 2625$

Calculate black shirts for S

Ratio of Black to White is $4:13$, sum of parts $= 4+13 = 17$. Black shirts in S $= (4/17) \times 3825 = 4 \times 225$.

$4 \times 225 = 900$

Find the average

Average $= (2025 + 2625 + 900) / 3 = 5550 / 3$.

$\frac{5550}{3} = 1850$