#### Answer

The estimated standard deviation is slightly more than the real standard deviation, but very close to it.

#### Work Step by Step

Range is the difference of the maximum and minimum of the set: range=49-12=37 minutes. Calculated by calculator, the mean is: 20.98 minutes. The variance is the sum of the differences of each value and the mean on the power of two, divided by the number of values minus 1: variance=$\frac{(30−20.98)^2+(19−20.98)^2+...+(30−20.98)^2}{48-1}=$85.5 minutes. The standard deviation is the square root of the variance: standard deviation=$\sqrt{85.5}=9.247$ minutes. By The Range Rule of Thumb the standard deviation is one fourth of the range:$\frac{37}{4}=9.25$ minutes. This estimated standard deviation is a littlebit more than the real standard deviation, but very close to it.