$\bar{x}_{\text{new}} = \bar{x}$ and $s_{\text{new}}^2 = \frac{(n-1)s^2 + 2c^2}{n+1}$

$\bar{x}_{\text{new}} = \bar{x}$ and $s_{\text{new}}^2 = \frac{ns^2 + 2c^2}{n+2}$

$\bar{x}_{\text{new}} = \bar{x} + c$ and $s_{\text{new}}^2 = s^2 + c^2$

$\bar{x}_{\text{new}} = \bar{x}$ and $s_{\text{new}}^2 = s^2 + \frac{2c^2}{n-1}$