Sabine records the daily heights of a random sample of bamboo stalks , in inches. They are: 20,19,17,16,18,15,20,21 Consider the formulas: A s^2=((x_(1)-bar (x))^2+(x_(2)-bar (x))^2+ldots +(x_(n)-bar (x))^2)/(n-1) B s=sqrt (((x_(1)-bar (x))^2+(x_(2)-bar (x))^2+ldots +(x_(n)-bar (x))^2)/(n-1)) c sigma ^2=((x_(1)-mu )^2+(x_(2)-mu )^2+ldots +(x_(N)-mu )^2)/(N) D: sigma =sqrt (((x_(1)-mu )^2+(x_(2)-mu )^2+ldots +(x_(N)-mu )^2)/(N)) Which formula should you use for variance? square Which formula should you use for standard deviation? square DONE

To determine which formulas to use for variance and standard deviation, we need to understand the difference between sample and population statistics.<br /><br />For a sample:<br />- Use formula A for variance: $s^{2}=\frac {(x_{1}-\bar {x})^{2}+(x_{2}-\bar {x})^{2}+\ldots +(x_{n}-\bar {x})^{2}}{n-1}$<br />- Use formula B for standard deviation: $s=\sqrt {\frac {(x_{1}-\bar {x})^{2}+(x_{2}-\bar {x})^{2}+\ldots +(x_{n}-\bar {x})^{2}}{n-1}}$<br /><br />For a population:<br />- Use formula C for variance: $\sigma ^{2}=\frac {(x_{1}-\mu )^{2}+(x_{2}-\mu )^{2}+\ldots +(x_{N}-\mu )^{2}}{N}$<br />- Use formula D for standard deviation: $\sigma =\sqrt {\frac {(x_{1}-\mu )^{2}+(x_{2}-\mu )^{2}+\ldots +(x_{N}-\mu )^{2}}{N}}$<br /><br />Since Sabine is recording the daily heights of a random sample of bamboo stalks, we should use the formulas for a sample.<br /><br />Therefore, the correct formulas to use are:<br />- For variance: Formula A<br />- For standard deviation: Formula B