According to the question

we know the formula,

Mean(Avg)=$\frac{\mathrm{Sum} \mathrm{of} \mathrm{observations} \left(\mathrm{S}\right)}{\mathrm{Number} \mathrm{of} \mathrm{observations} \left(\mathrm{N}\right)}$

Given, Mean (Avg) = 28, N= 10

⇒ $28=\frac{\mathrm{S}}{10}$= 280

Later, it was discovered that one observation 14 was misread as 24

= 24-14= 10

∴ The correct mean is

 $$\begin{gathered} =\frac{\mathrm{S}-10}{\mathrm{N}} \\ =\frac{280-10}{10} \\ =\frac{270}{10}=27 \end{gathered}$$

Hence, Option C is correct.