2015 Year 11 Mathematical Applications
Directed Investigation
Statistics

Lani Cheetham
DSECK
Contents page
Introduction pg. 3 & 4

Mathematical Investigation pg. 4-11

Frequency tally (Fitness) pg. 5

Frequency tally (social Network) pg. 6

Mean, Mode & Median (Fitness) pg. 7

Mean, mode and median (social network) pg. 8

Back to back ordered Stem Leaf Plot pg. 9

Box & Whisper Plot (both sets) pg. 10

Histogram (both sets) pg. 11

Conclusion pg. 12

Appendix 1 pg. 13

Introduction:
The purpose of this directed investigation was to show the understanding and knowledge of statistics. This specific task demonstrates the skill learnt in regards to gathering, sorting and placing information into the different aspects of Statistics. The directed investigation focuses primarily on the topic statistics which includes mathematically finding the mean, mode, and median, creating a stem and leaf plot as well as a box plot on the survey that was put together on a topic of choice. All of these are presented in the following investigation. The directed investigation was divided into around five parts.
The investigation was conducted by first putting together a survey of choice and sending out to a selected group. The survey was sent to year 9-11 Gleeson students. The survey chosen was on Fitness. It consisted of four questions. Questions one and two were multiple choice were the participants in the survey choice what suited them. Question one was what year level are you in? And question two was what gender are you? Question 3 and 4 were question that involved writing an answer. Question 3 was ‘How many hours of fitness do you weekly? And question 4 was how many hours a week do you spend on social networking sites, watching television and listening to music.

It is ideal to get between 30 to 50 useful responses to your survey to be able to continue. After collecting all information from the surveys the next step is to go through and mathematically collect the mean, mode and median from the collected information. The mean is found by adding all values together and dividing them by the amount of values. This is done twice in this directed investigation to find one for both sets of data. The mode is the most frequent occurring number/s in the set of data. The median is found by using the equation (n+1) ÷2, which is taking the amount of values then adding one and dividing that number by two. This will give the number of the set of data that your median is . The next step is to use the mean, mode and median to create an ordered stem and leaf plot, using a stem and leaf plot you are able to find the mean mode and median easier and faster. This step is then followed by a box plot containing the collated information. The use of technology, such as a Casio scientific calculator and Microsoft word & Microsoft Excel was implemented to assist in the calculation of this investigation. Survey Monkey was used to help create the survey template and the Gleeson College email was useful in helping to easily send out the survey to the selected group. Findings were presented electronically with the use of Microsoft word.

Mathematical Investigation
Firstly it involved finding a question to base the survey on. This directed investigation was based around the hours of fitness partaken by 75 students between the years of 9-11 in comparison to the amount of time that the same 75 students spent on social networking sites. The survey was sent out and responses were returned.

The information was then summarised using two-frequency tally’s. One