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:

\(\begin{array}{c}\bar x = \frac{{51 + 44 + ........ + 23}}{{14}}\\ = 37.1\end{array}\)

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:

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

Therefore, the median value is equal to 36.0 deaths.

c.

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

\(\begin{array}{c}s = \sqrt {\frac{{\sum\limits_{i = 1}^n {{{({x_i} - \bar x)}^2}} }}{{n - 1}}} \\ = \sqrt {\frac{{{{\left( {51 - 37.1} \right)}^2} + {{\left( {44 - 37.1} \right)}^2} + ....... + {{\left( {23 - 37.1} \right)}^2}}}{{14 - 1}}} \\ = 9.8\end{array}\)

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:

\(\begin{array}{c}{s^2} = \frac{{\sum\limits_{i = 1}^n {{{({x_i} - \bar x)}^2}} }}{{n - 1}}\\ = \frac{{{{\left( {51 - 37.2} \right)}^2} + {{\left( {44 - 37.2} \right)}^2} + ....... + {{\left( {23 - 37.2} \right)}^2}}}{{14 - 1}}\\ = 96.8\end{array}\)

Therefore, the sample variance is equal to 96.8 deaths.

e.

The range of the number of deaths is computed below:

\(\begin{array}{c}{\rm{Range}} = {\rm{Maximum}}\;{\rm{value}} - {\rm{Minimum}}\;{\rm{value}}\\ = 51 - 23\\ = 28.0\end{array}\)

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.