On Monday evening 27 September I joggled laps of the PICS track in lane four. Joggling is juggling while running. Each and every lap I counted the number of throws I made with my right hand. I also timed my laps. The first part of the midterm uses the number of right hand throws I made per lap for ten laps.
_________ What level of measurement is the data?
__________ Calculate the sample size n for the data.
__________ Determine the minimum.
__________ Determine the maximum.
__________ Calculate the range.
__________ Calculate the midrange.
__________ Determine the mode.
__________ Determine the median.
__________ Calculate the sample mean x.
10.27 Freebie: This is the standard deviation sx.
If you obtain a different value, then you typed in the wrong data!
Calculate the standard deviation sx and check for agreement. [10.2681 to four decimal places]
__________ Calculate the sample coefficient of variation CV.
__________ If this data were to be divided into four classes, what would be the width of a single class?
Determine the frequency and calculate the relative frequency using four classes.
Record your results in the table provided.
Frequency table
Riders CUL (cm)
Frequency (f)
Relative Frequency
Sum:
Sketch a frequency histogram chart of the data anywhere it fits, labeling your horizontal axis and vertical axis as appropriate.
____________________ What is the shape of the distribution?
__________ On the ninth lap I dropped my throw height down to 30 centimeters, which resulted in a 2:02 lap on which I made 178 throws from my right hand. Use the sample mean x and standard deviation sx calculated above to determine the z-score for 178 throws.
____________________ Is the z-score for 178 an ordinary or unusual z-score?
__________ On the tenth lap I increased my throw height up to 50 centimeters, which resulted in a 2:54 lap on which I made 205 throws from my right hand. Use the sample mean x and standard deviation sx calculated above to determine the z-score for 205 throws.
____________________ Is the z-score for 205 an ordinary or unusual z-score?
Part II: Linear regression
For each and every lap I recorded the lap time for that lap. This section explores whether there is a relationship between my lap time and the number of throws I made from my right hand. I ran in lane four, which is 427 meters long. The times are the time for one lap. Smaller times are faster.
Time (min)
Throws
2.5
189
2.5
198
2.6
196
2.0
178
2.9
205
__________ Calculate the slope of the linear regression for the data.
__________ Calculate the y-intercept of the linear regression for the data.
__________ Use the slope and intercept to predict the number of throws for a lap of 2.3 minutes.
__________ Use the slope and intercept to predict the time for a lap with 185 throws.
__________ Does the relationship appear to be linear, non-linear, or random?
__________ Is the correlation positive, negative, or neutral?
__________ Calculate the correlation coefficient r.
__________ What is the strength of the correlation: strong, moderate, weak, or none?
__________ Calculate the coefficient of determination r².
__________ What percent of the variation in the lap time in minutes
explains the variation in the number of throws?
I can control the height I throw my tennis balls while running and juggling. The higher I throw the tennis ball, the longer the ball is in the air. I usually throw my tennis balls about 40 centimeters high. For example, when I threw the balls 50 centimeters high, I made 205 throws during a 2:54 lap (2.9 minutes). When I threw the balls lower, only 30 centimeters high, I made only 178 throws during a faster 2:02 lap (2.0 minutes). Does the correlation and coefficient of determination provide support for the theory that I can control my speed by how high I throw the tennis balls? Why or why not?