Characteristic strength of concrete cubes

Characteristic strength is the strength below which not more than 5% of the test results are expected to fall (IS 456, Terminology).

Formula: characteristic strength (95% confidence) $f_{ck} = f_m - 1.65\,s$, with the sample standard deviation $s = \sqrt{\sum(x-f_m)^2/(n-1)}$. The factor 1.65 comes from the normal distribution (the same factor is used in mix design, $f_{target} = f_{ck} + 1.65\,s$, IS 10262). Assumptions: the results follow the normal distribution, and the sample standard deviation ($n-1$) is used.

$n = 11$, $\sum x = 263$, mean $f_m = 263/11 = 23.91$ N/mm$^2$.

$$\begin{aligned} s &= \sqrt{\frac{82.91}{11-1}} = 2.879\ \text{N/mm}^2 \\ f_{ck} &= 23.91 - 1.65\times2.879 = 19.16\ \text{N/mm}^2 \end{aligned}$$

Answer: characteristic strength $f_{ck} \approx$ 19.2 N/mm$^2$.