If all the observations in a data set are increased by 5, the mean ____.

**Assumed mean**: pick a value 'a' close to the centre. Compute deviations dᵢ = $x$ᵢ − a.

**Formula**: **$x$̄ = $a$ + Σ(fᵢdᵢ) / Σfᵢ**

This simplifies arithmetic when class marks are large.

**Step-deviation method**: when all class widths equal $h$, define uᵢ = $(x$ᵢ − a)/$h$.

**Formula**: **$x$̄ = $a+h$ × [Σ(fᵢuᵢ) / Σfᵢ]**

This turns class marks into small integers (e.g., −2, −1, 0, 1, 2) — much easier arithmetic.

**All three methods give the same mean** — choose by convenience.