91影视

The stem and leaf diagram for the two machines is given below

Range = Maximum - Minimum

Median $={(\frac{n+1}{2})}^{th}term$

For machine $A$

Minimum value $=14$

Maximum value $=46$

Range $=46-14$

Range $=32$

Median

$n=15$

Median$={(\frac{15+1}{2})}^{th}term$

$Q^2=8^{th}term=28$

Skewness

Most of the data values are between $20鈭�29$

It seems to be symmetric roughly.

For machine $B$

Minimum value = $2$

Maximum value = $59$

Range = $59-2$

Range $=57$

$n=15$

$Q_2=8^{th}term=38$

Skewness

Most of the data values are between $30鈭�39$

It appears to be negatively skewed, as it leans to the left.

Center

Center can be compared on the basis of the median.

Here, Machine $A(=28)<MachineB(=38)$

Spread

Machine $B$is more spread than machine $A$in this case because its range is bigger than machine $A\text{'}s$

Skewness

Machine $A$is roughly symmetrical while Machine $B$is negatively skewed.

$\overline{x}=\frac{危x}{n}$

The machine with the greatest overall gain can be determined based on the average increase in cardiovascular fitness.

For machine A

$$\begin{gathered} \overline{A}=\frac{危A}{n} \\ \overline{A}=\frac{14+15+..................................46}{15} \\ \overline{A}=\frac{434}{15} \\ \overline{A}=28.9333 \end{gathered}$$

For machine $B$

$$\begin{gathered} \overline{B}=\frac{危B}{n} \\ \overline{B}=\frac{2+10+.............................+59}{15} \\ \overline{B}=\frac{531}{15} \\ \overline{B}=35.4 \end{gathered}$$

Mean overall gain is higher in machine $B$

$s^2=\frac{1}{n-1}脳\left(危x^2鈭�n脳{\overline{x}}^2\right)$

Variance can be used to assess consistency.

More volatility indicates a lack of stability.

For machine $A$

$$\begin{gathered} {s_A}^2=\frac{1}{15-1}脳\left(危A^2-n脳{\overline{A}}^2\right) \\ 危A^2={14}^2+{15}^2+......{46}^2=13788 \\ {s_A}^2=\frac{1}{15-1}脳\left(13788-15脳{28.9333}^2\right) \\ {s_A}^2=87.9259 \end{gathered}$$

For machine $B$

$$\begin{gathered} {s_B}^2=\frac{1}{15-1}脳\left(危B^2-n脳\overline{B^2}\right) \\ 危B^2=2+10+.........59=22469 \\ {s_B}^2=\frac{1}{15-1}脳\left(22469-15脳{35.4}^2\right) \\ {s_B}^2=262.2571 \end{gathered}$$

The variance of machine $B$is greater than machine $A$

Volunteers are picked from the surrounding area of the company's headquarters. This may not be representative of the total cardiovascular fitness gain population. The outcomes of other centers may differ.