魅影直播

The data showed the frequencies of the best actors according to their ages when they won the Oscar. The ages are grouped into 7 class intervals.

The formula for calculating thestandard deviation of a frequency distribution is expressed as follows:

$s=\sqrt{\frac{n\left[鈭�\left(f脳x^2\right)\right]-{\left[鈭�\left(f脳x\right)\right]}^2}{n\left(n-1\right)}}$

Here, f denotes the frequencies;

x denotes the midpoints of the class intervals;

n denotes the total frequency.

The table below shows the necessary calculations:

The value of standard deviation is calculated as follows, using the values obtained above:

$$\begin{gathered} s=\sqrt{\frac{n\left[鈭�\left(f脳x^2\right)\right]-{\left[鈭�\left(f脳x\right)\right]}^2}{n\left(n-1\right)}} \\ =\sqrt{\frac{87\left(180281.75\right)-{\left(3871.5\right)}^2}{87\left(87-1\right)}} \\ =9.6 \end{gathered}$$

Therefore, the computed standard deviation is equal to9.6 years.

The actual value of standard deviation is 8.9 years.

Thus, the standard deviation computed from the sample is 9.6 years, which isquite close to the actual value equal to 8.9 years.