91影视

The mean of five pulse rates is 78.0 beats per minute.

The four known observations are 82, 78, 56, and 84.

a.

Let c be the missing pulse rate observation.

The formula for the mean of n observations is stated as follows.

$\stackrel{炉}{x}=\frac{鈭�x}{n}$ for n observation with values x.

Substitute the pulse rates observation in the formula as shown.

$$\begin{gathered} 78=\frac{82+78+56+84+c}{5} \\ 78=\frac{300+c}{5} \\ 390=300+c \\ c=90 \end{gathered}$$

Thus, the missing observation is 90 beats per minute.

b.

It is required to list n values for a known mean measure.

The degree of freedom is the number of values that are free to be selected from n.

For the mean value of $\stackrel{炉}{x}$ for n counts of observations, the sum of all observations is defined as $\underset{i=1}{\overset{n}{鈭�}}x$, such that the formula holds true.

$\stackrel{炉}{x}=\frac{{鈭�}_{i=1}^{n}x}{n}$is the known sum of all observations. It can be true for many possible combinations of observations.

To determine a feasible combination, you can select n 鈥� 1 observations freely (randomly), but the last observation will always be$\underset{i=1}{\overset{n}{鈭�}}{x}_i-\underset{i=1}{\overset{n-1}{鈭�}}{x}_i$ .

As a result, there are only n 鈥� 1 observations free to be chosen.

Thus, the degree of freedom is n 鈥� 1.