Q 3.29. - 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.

 Daily Motorcycle Accidents. The Scottish Executive, Analy. tical Services Division Transport Statistics, compiles data on motor cycle accidents. During one year, the numbers of motorcycle accidents in Scotland were tabulated by day of the week for built-up roads and non-built-up roads and resulted in the following data .

a. Find the mean and median of the number of accidents for built-up roads. 

b. Find the mean and median of the number of accidents for non built-up roads. 

c. If you had a list of only the day of the week for each accident, what day would be the modal day for each type of road? 

d. What might explain the difference in the modal days for the two types of roads?

Step-by-Step Solution

Answer

a) Mean$=88.43$  ,Median$=88$

b) Mean $=70.3$,Median$=59$

c) The modal day for road construction would be Friday, and the modal day for non-construction would be Sunday.

d) The total number of motorcycle accidents that occurred in a given year. Friday is a workday, so commuters utilising the build-up roads are more likely to be involved in accidents; notice that Friday has the second lowest number of accidents on non-build-up routes.

Sunday is a day when rides in the countryside off the paved roads are more likely to be crushing; remember that Sunday has the lowest number of accidents on the paved roads.

Step 1. Given information.

We have given data for build up:$88, 100, 76, 98, 103, 85, 69.$

and non build up:$70, 58,59, 53, 56, 94, 102.$

Part a) Step 1. Mean of the data.

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

$$\begin{gathered} =\frac{88+100+76+98+103+85+69}{7} \\ =88.4285 \\ =88.43 \end{gathered}$$

Part a) Step 2. Median of the data.

Arrange the data in increasing order :$169, 76, 85, \left(88\right), 98, 100, 103$

The number of observation is $7$.

The median is the  middle observation in the ordered list. 

Median is $88$.

Part b) Step 1. Mean of the data

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

$$\begin{gathered} =\frac{ 70+ 58+59+ 53+ 56+ 94+ 102}{7} \\ =70.28 \\ =70.3 \end{gathered}$$

Part b) Step 2. Median of the data.

Arrange the data in increasing order: $53, 56, 58, \left(59\right), 70, 94, 102$.

The number of observation is $7$.

The median is the  middle observation in the ordered list. 

Median is $59$.

Part c) Step 1. To find list of only the day of the week for each accident for each type of road?

The number of motorcycle accidents in during 1 year Friday would be the modal day for build up roads and Sunday would be the modal day for non-build up roads. 

Part d) Step 1. Explain the difference in the modal days for the two types of roads

In a particular year, the total number of motorcycle accidents that happened. Because Friday is a workday, commuters using the build-up roadways are more likely to be involved in accidents; however, non-build-up routes have the second lowest number of accidents.

Sunday is a day when rides in the countryside off paved roads are more likely to be harrowing; keep in mind that Sunday has the fewest paved road accidents.