91影视

Data are given on the number of deaths that have occurred due to lightning strikes for a series of 14 consecutive years.

a.

Let x be the number of deaths due to lightning strikes.

The mean number of deaths that have occurred due to lightning strikes is computed:

$$\begin{gathered} \stackrel{炉}{x}=\frac{51+44+........+23}{14} \\ =37.1 \end{gathered}$$

Thus, the mean value is equal to 37.1 deaths.

b.

The data is arranged in ascending order as follows:

As the number of data values present is even (14), the following formula is used to compute the median value:

$$\begin{gathered} \text{Median}=\frac{{\left(\frac{n}{2}\right)}^{th}obs+{\left(\frac{n}{2}+1\right)}^{th}obs}{2} \\ =\frac{{\left(\frac{14}{2}\right)}^{th}obs+{\left(\frac{14}{2}+1\right)}^{th}obs}{2} \\ =\frac{7^{th}obs+8^{th}obs}{2} \\ =\frac{34+38}{2} \\ =36 \end{gathered}$$

Therefore, the median value is equal to 36.0 deaths.

c.

The sample standard deviation of the number of deaths is computed below:

$$\begin{gathered} s=\sqrt{\frac{{鈭�}_{i=1}^n{(x_i-\stackrel{炉}{x})}^2}{n-1}} \\ =\sqrt{\frac{{\left(51-37.1\right)}^2+{\left(44-37.1\right)}^2+.......+{\left(23-37.1\right)}^2}{14-1}} \\ =9.8 \end{gathered}$$

Therefore, the value of the standard deviation is equal to 9.8 deaths.

d.

The sample variance of the number of deaths is computed below:

$$\begin{gathered} s^2=\frac{{鈭�}_{i=1}^n{(x_i-\stackrel{炉}{x})}^2}{n-1} \\ =\frac{{\left(51-37.2\right)}^2+{\left(44-37.2\right)}^2+.......+{\left(23-37.2\right)}^2}{14-1} \\ =96.8 \end{gathered}$$

Therefore, the sample variance is equal to 96.8 deaths.

e.

The range of the number of deaths is computed below:

$$\begin{gathered} \text{Range}=\text{Maximum}\text{value}-\text{Minimum}\text{value} \\ =51-23 \\ =28.0 \end{gathered}$$

Therefore, the range is equal to 28.0 deaths.

f.

The gradual change in the number of deaths due to lightning strikes over the years is not depicted by the computed statistics.

A time-series graph showing the trend of the values over 14 years would be an appropriate tool.