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.
Riders CUL (cm)
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.
__________ 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?