Rather than multiplying frequencies by the full class marks (110, 130, …), we take a convenient assumed mean $A$ and work with the much smaller deviations from it.

We use the assumed mean method: $\bar{x} = A + \dfrac{\sum fd}{\sum f}$, where $d = x - A$ and $A$ is a conveniently chosen class mark.

Step 1 — Find the class marks and choose $A$. Class marks: $110, 130, 150, 170, 190$. Choose $A = 150$ (the middle class mark, also the one with the highest frequency, 15 — an ideal choice since it keeps the deviations small and symmetric).

Step 2 — Compute deviations $d = x - A$ and $fd$.

$\sum fd = -320-240+0+200+200 = -160$.

Step 3 — Apply the formula. …

Forgetting to add $A$ back at the end (stopping at $\sum fd/\sum f = -3.2$ and calling that the mean) is the classic mistake — the assumed mean method finds a deviation from $A$, which must always be added back to $A$ its …