REVIEW from Chapter 1 : Key Elements of a Statistical Problem Describe the population Describe the variable/s of interest Describe the sample Describe the inference Describe sources of possible errors/bias 1
1: Speed Training Program for High School Football players Michael Gray and Jessica Sauerbeck researchers at Northern Kentucky University designed and tested a speed training program for a junior-varsity and varsity high school football players. Each participant was timed in a 40-yard sprint prior to the start of the training program and timed again after completing the program. Based on these sprint times, each participant was classified as having an improved time, no change in time, or a decrease in time. In a sample of 15 players selected from different schools in the area, 13 had an improved time. The results show that nearly 87% (=13/15%) of players who participated in this speed training program improved their sprint times. 2
2 Does a message enable the muscles of a tired athletes to recover faster than usual? To answer this question researchers recruited eight amateur boxers to participate in an experiment. After a 10-minute workout in which each boxer threw 400 punches, half the boxers were given a 20 minute message. The other half rested. Before returning to the ring for a second workout, the heart rate and blood lactate level were recorded for each boxer. The researchers found no difference in the means of the two groups of boxers for either variable. 3
Chapter 2: Descriptive Statistics Two types of variables Qualitative Quantitative There are different ways to represent each type of Data, but we will find there are more techniques for describing Quantitative data. 4
Qualitative Data To describe Qualitative data we must place the data into a certain classes. Each class has an associated class frequency and relative frequency and class percentage. Sometimes we keep track of these cumulatively. 5
A total of 22 StFX students were tested and found to have the following blood types: O O A A A A A A A A A A A B B B B B AB AB AB AB Classes Blood Type 0 2 A 11 B 5 AB 4 is how often each class occurs 6
A total of 22 StFX students were tested and found to have the following blood types: Blood Type Cumulative 0 2 2 A 11 13 B 5 18 AB 4 22 is how often each class occurs 7
A total of 22 StFX students were tested and found to have the following blood types: Blood Type Relative 0 2 2/22 = 0.0909 A 11 11/22 = 0.5000 B 5 5/22 = 0.2273 AB 4 4/22 = 0.1818 Realtive n 8
A total of 22 StFX students were tested and found to have the following blood types: Blood Type Rel freq. 0 2 0.0909 A 11 0.5000 B 5 0.2273 AB 4 0.1818 Percentage *100% n Relativefrequency Percentage % 9.09% 50.00% 22.73% 18.18% 9
A total of 22 StFX students were tested and found to have the following blood types: Blood Type Percentage Percentage Cumulative Percentage 0 2 9.09 9.09 A 11 50.00 59.09 B 5 22.73 81.82 AB 4 18.18 100.00 n *100 10
Qualitative Data With qualitative data (and any other data we wish to separate into certain classes), tables, charts and diagrams are often the best way to present the data. It gives us a visual feel for the data and pictures can be more easily understood quickly and information can be passed on without technical jargon. 11
A total of 22 StFX students were tested and found to have the following blood types: Blood Type Percentage Cumulative Percentage 0 2 9.11 9.11 A 11 50.00 59.11 B 5 22.70 81.72 AB 4 18.28 100.00 12
Pie Chart Student Blood Types 9.1 18.2 A B 50 AB O 22.7 13
Bar Graph Student Blood Types 12 11 9.6 7.2 4.8 4 5 2.4 2 0 A B AB O Blood Type In bar graph, the height of each bar is the class frequency. 14
Histogram Student Blood Types 12 11 9.6 7.2 4.8 4 5 2.4 2 0 A B AB O Blood Type We may also ask you to draw a histogram where the height of each bar is the class frequency or class percentage. 15
Pareto Graph It is a bar graph arranged from highest to lowest. 12 10 8 6 4 2 0 A B AB O 16