Question

Monthly Motorcycle Casualties. This Scottish Executive Analytical Services Division Transport Statics. compiles data on motorcycle accidents .During one year, the numbers of motorcycle accidents in Scotland were tabulated by day of the week for built up road and non built up road were as follows,

Part (a) Without doing any calculations, make an educated guess at which of the two data sets, built up or non built or non built up has the greater variation.

Pat (b) Find the range and sample standard deviation of each of the two data sets, Compare your results here to the education guess that you made in part (a)

Short answer

Part (a) The variation in the non-build-up data set is greater.

Part (b) The given data has a range and standard deviation of 34 and 12.8, respectively.

Step-by-step solution

Part (a) Step 1. Given information.

The set's data points are:

800, 100, 76, 98, 103, 85, 69.

Part (a) Step 2. The data has a greater variation.

A data set's range is given by range = max-min.

The formula computes the standard deviation.

$s=\sqrt{\frac{\sum _{}{x_i}^2-{\left(\sum _{}{x}_i\right)}^2/n}{n-1}}$

Because it has the same maximum and lower minimum as the build-up data set, it has more variation.

As a result, the non-build-up data set has more variation.

Part (b) Step 1. Given information.

The set's data points are:

800, 100, 76, 98, 103, 85, 69.

Part (a) Step 2. The range and standard deviation of the given data.

A data set's range is given by range = max-min.

The formula computes the standard deviation.

$s=\sqrt{\frac{\sum _{}{x_i}^2-{\left(\sum _{}{x}_i\right)}^2/n}{n-1}}$

A data set's range is given by range = max-min.

Range

$$\begin{gathered} =103-69 \\ =34 \end{gathered}$$

As a result, the data set's range is 34.

The mean of the given data set.

$$\begin{gathered} \overline{x}=\frac{88+100+76+98+103+85+69}{7} \\ \overline{x}=\frac{619}{7} \\ \overline{x}=88.4286 \end{gathered}$$

Standard deviation

$$\begin{gathered} \sigma =\sqrt{\frac{\sum _{}{\left(x_i-\overline{x}\right)}^2}{n-1}} \\ \sigma =\sqrt{\frac{981.7143}{7-1}} \\ \sigma \approx 12.7914 \end{gathered}$$

As a result, the given data's range and standard deviation are 34 and 12.8, respectively.