Question

Lacrosse is one of the oldest sports in North America. Despite its long history, it is a very dangerous contact sport comparable with football and ice hockey. Lacrosse involves inherent impact to participants and the National Collegiate Athletic Association (NCAA) stated that head injuries account for approximately 13% of all game-related injuries in the sport. Head injuries and repetitive head impacts can cause cumulative damage and chronic neurologic problems. Helmets are required in the sport but around 2000, there were several versions of helmets allowed with no mention of which version would offer the greatest level of protection. Some of these helmet types were deemed ‘Traditional’ while some were newer, more lightweight and considered to be ‘Contemporary’. These helmets are designed to take impact from all directions but two specific impact sites are of particular interest: a head-on collision where impact is received from the ‘Front’ and a blind-side impact where impact is received from the ‘Rear’.

A researcher interested in head injury prevention and lacrosse helmet protection, attempted to study which version of helmet was best in different impact situations. In order to have a quantitative measure of impact severity, the Gadd Severity Index (GSI) was used by the researcher. Note that higher GSI scores correspond to more severe impacts and, consequently, lower GSI scores are preferable.

(2) Using the StatCrunch output stated bellow, state initial conclusions that could be made in two to four complete sentences.

the Data:

I) Two measures of center and two measures of variation for the sample overall

2 measures of center

Mean              Median                      

1154.1125        1110.47                 

2 measures of variation

Variance          Std. dev.

62462.103          249.92419

ii) Two measures of center and two measures  of variation for the sample ‘grouped by’ helmet type (i.e. contemporary and traditional).

data

2 measures of center

Mean              Median

Contemporary                     1070.0749            1065.26

Traditional                             1238.1501            1288.002

                                    2 measures of variation

Variance        Std. dev.

Contemporary                     25801.136        160.62732

Traditional                             86237.861        293.66283

iii) Two measures of center and two measures of variation for the sample ‘grouped by’ impact site (i.e. front and rear).

2 measures of center

Mean              Median

Back                                           1217.35            1115.797

Front                                          1090.875               1093.975

                                    2 measures of variation

Variance        Std. dev.

Back                                          73260.9            270.66751

Front                                          45061.863        212.2778

Answer 1

1) For the overall sample The mean and median is 1154.1125 and 1110.47. Note that mean takes into consideration of all points where as the median leaves the extreme points. So looking at the median is sometimes efficient. And the standard deviation i.e, the overall spread is  249.92419.

2) Overall sample grouped by helmet (Contemporary and Traditional )

The mean for contemporary and Traditional is 1070.0749 and 1238.1501 respectively.

The median for contemporary and Traditional is 1065.26 and 1288.002 respectively.

The standard deviation for contemporary and Traditional are 160.62732 and 293.66283 respectively.

The mean and median of the contemporary helmet is almost same and deviation is also less.

3) Sample grouped by impact side( back and front)

The mean for back and front are 1217.35 and 1090.8750 respectively.

The median for back and front are 1115.797 and 1093.975 respectively.

The standard deviation for back and front are 270.66751 and 212.2778 respectively.

Note that spread of back injuries are more and so the mean is.

Overall the back injuries are more in the sample.