In a school experiment a student fixes a small bright object on an optical bench and moves a convex…

Step 1. The first pair. We want $f$, so $\dfrac{1}{f} = \dfrac{1}{v} - \dfrac{1}{u} = \dfrac{1}{100.4} + \dfrac{1}{25.0} = 0.04996\ \text{cm}^{-1}$. So $f = 20.02\ \text{cm}$.

Step 2. All five pairs. The values are $20.02$, $19.96$, $20.12$, $19.92$ and $20.09$ centimetre.

Step 3. The mean. The five values add up to $100.11\ \text{cm}$. So $\bar{f} = \dfrac{100.11\ \text{cm}}{5} = 20.02\ \text{cm}$.

Step 4. The spread. The largest value is $20.12\ \text{cm}$ and the smallest is $19.92\ \text{cm}$. The difference is $0.20\ \text{cm}$, which is $\dfrac{0.20}{20.02} = 1.0\ \%$ of the mean.

Step 5. The straight line. Plot $\dfrac{1}{v}$ against $\dfrac{1}{u}$. The points lie close to a line of slope $1$. Its intercept is $\dfrac{1}{f} = 0.0498\ \text{cm}^{-1}$, so $f = 20.1\ \text{cm}$.