Find the standard deviation of 5.58, 5.53, 6.19, 5.66, 5.87, 5.62.

Step-by-step solution

1. 1

   Find the mean and keep extra digits.

   $\bar{x} = \frac{34.45}{6} = 5.741\overline{6} \approx 5.74167$

   This mean does not terminate, so carrying only two decimals ($5.74$) would visibly shift the squared deviations. Keep four or five digits until the very end.

2. 2

   Square each deviation from the mean.

   $(5.58 - 5.74167)^2 \approx 0.02614, \quad (5.53 - 5.74167)^2 \approx 0.04480$

   $(6.19 - 5.74167)^2 \approx 0.20100, \quad (5.66 - 5.74167)^2 \approx 0.00667$

   $(5.87 - 5.74167)^2 \approx 0.01647, \quad (5.62 - 5.74167)^2 \approx 0.01480$

3. 3

   Add the squared deviations.

   $\sum (x - \bar{x})^2 \approx 0.30988$

   Notice that $6.19$ alone contributes $0.201$ of that total — about two thirds. A single value far from the mean dominates the variance because the deviation is squared.

4. 4

   Divide by n − 1 for the sample variance. With $n = 6$ values treated as a sample:

   $s^2 = \frac{0.30988}{5} \approx 0.06198$

   If the six values were the whole population you would divide by $6$ instead, giving $\sigma^2 \approx 0.05165$.

5. 5

   Take the square root.

   $s = \sqrt{0.06198} \approx 0.2490$

   So the sample standard deviation is about $0.249$ (the population value would be $\sigma \approx 0.227$). Rounded to two decimals the sample answer is $0.25$.