This is a discrete frequency distribution, so the mean is the frequency-weighted average $\sum fx/\sum f$, not a plain average of the six listed numbers.

$\sum fx = 110$, $\sum f = 50$

$\bar{x} = \dfrac{110}{50} = 2.2$

This is a discrete frequency distribution (values $x$ = number of children, against frequencies $f$ = number of families), so we use $\bar{x} = \dfrac{\sum fx}{\sum f}$.

Step 1 — Compute $fx$ for each row.

Step 2 — Sum the columns. $\sum f = 5+10+15+12+6+2 = 50$ (matches the stated 50 families — a useful cross-check). $\sum fx = 0+10+30+36+24+10 = 110$.

Step 3 — Divide.

Independent check. Re-adding the $fx$ column in a different order: $(10+24)+(30+36)+(0+10) = 34+66+10 = 110$ — confirms the total.

A frequent error is averaging only the six $x$-values (getting 2.5) while ignoring how many families each value represents — the mean here must be frequency-weighted. Always confirm $\sum f$ equals the total number of observations stated in the question (here, 50 families) as a built-in check.