Q 3.28 - Elementary Statistics

Question

Find the 

a. Mean    b. median      c. mode

For the mean and the median, round each answer to one more decimal place than that used for the observations

Monthly Motorcycle Casualties. The Scottish Executive, Analytical Services Division Transport Statistics, compiles data on motorcycle casualties. During one year, monthly casualties from motorcycle accidents in Scotland for built-up roads and non-built-up roads were as follows 

a) Find the mean, median, and mode of the number of motorcycle casualties for built-up roads.

b) Find the mean, median, and mode of the number of motorcycle casualties for non built-up roads. 

c) If you had a list of only the month of each casualty, what month would be the modal month for each type of road?

Step-by-Step Solution

Answer

$a)$ Mean$=52.67$, Median $=51.5$, Mode$=38$

b) Mean$=44.5$, Median$=38$, Mode does not exist.

c)August would be the modal month for built-up causality if each casualty had its own month. For non-built-up causality, July will be the modal month.

Step 1. Given information.

We have given data for build up : $25, 38, 38, 56, 61, 52, 50, 90, 67, 51, 64, 40$

and non build up :$16, 9, 26, 48, 73, 72, 91, 69, 71, 28, 19, 12$

Part a) Step 1. Mean of the data.

Mean $=\frac{Sum of observation }{Number of observation}$

$$\begin{gathered} =\frac{25+ 38+ 38+ 56+ 61+ 52+ 50+ 90+ 67+ 51+ 64+ 40}{12} \\ =\frac{632}{12} \\ =52.67 \end{gathered}$$

Part a) Step 2. Median of the data.

Arrange the data in increasing order : $25,38,38,40,50,51,52,56,61,64,67,90$

The number of items are even. So, 

Median

$$\begin{gathered} =\frac{51+52}{2} \\ =51.5 \end{gathered}$$

Part a) Step 3. Mode of the data.

The greatest frequency is the mode of the data set. 

The mode of the given data set is$38$.

Part b) Step 1. Mean of the data.

Mean$=\frac{Sum of observation }{Number of observation}$

$$\begin{gathered} =\frac{16+9+26+48+73+72+91+69+71+28+19+12}{12} \\ =\frac{534}{12} \\ =44.5 \end{gathered}$$

Part b) Step 2. Median of the data.

Arrange the data in increasing order : $9, 12,46,19,26,28,48,69,71,72.73,91$

The number of observation is $12$.

Median

$$\begin{gathered} =\frac{28+48}{2} \\ =38 \end{gathered}$$

Part a) Step 3. Mode of the data.

The greatest frequency is the mode of the data set. 

There is no mode for given data set.

Part c) Step 1. To find what month would be the modal month for each type of road casualty ?

If each casualty had its own month, August would be the modal month for built-up causality. July will be the modal month for non-built-up causation.