As price rises, quantity demanded falls consistently, so a strong negative correlation is expected before any calculation.

$\bar x=30,\bar y=26$. $\sum(x-\bar x)(y-\bar y)=-750$; $\sum(x-\bar x)^2=1000$; $\sum(y-\bar y)^2=570$.

$r = -750/\sqrt{1000\times570} \approx -0.993$.

Step 1 — Find the means. $\bar x = \dfrac{10+20+30+40+50}{5}=30$. $\bar y = \dfrac{40+35+25+20+10}{5}=26$.

Step 2 — Tabulate deviations, products and squares.

Step 3 — Apply the formula.

Independent check. Every single week shows price rising alongside demand falling — a perfectly consistent pattern — so an $r$ this close to $-1$ is exactly what should be expected; a value near $0$ or positive would signal an arithmetic error. Also, re-summing the cross-product column in reverse order, $(-320-60)+(0-90-280) = -380-370=-750$ — matches, confirming the total.

Reporting the correlation as positive by misreading the table (both columns appear to be 'changing' left to right, and it is easy to overlook that $y$ is actually decreasing while $x$ increases) — always explicitly check the direction of $y$'s movement as $x$ rises, not just that both are changing.