When I juggle and run, a sport called joggling, the height of my tennis ball tosses influences the cadence at which I run - the rate at which my legs turn-over. This in turn influences my speed. This midterm focuses on the height of my tennis ball throws versus my time to complete one lap of the PICS track in lane three (about 420 meters - only the inside of lane one is 400 meters). For the first nineteen questions, use the data in table one.
n= __________ Calculate the sample size n.
Q0 = __________ Calculate the minimum (zeroth quartile).
Q1 = __________ Calculate the first quartile.
Q2 = __________ Calculate the median (second quartile).
Q3 = __________ Calculate the third quartile.
Q4 = __________ Calculate the maximum (fourth quartile).
IQR = __________ Calculate the Inter-Quartile Range.
Make a sketch of the box plot for this time data.
x = __________ Calculate the sample mean x.
mode = __________ Calculate the mode.
sx = __________ Calculate the sample standard deviation sx.
CV = __________ Calculate the sample coeficient of variation CV.
z = __________ Calculate the z-score for 63 centimeters.
range = __________ Calculate the range.
width = __________ If the time data is divided into three classes, what is the width of a single class?
Determine the frequency and calculate the relative frequency for the data.
Record your results in the table provided.
Class upper limits
Sketch a frequency histogram for the data, labeling your horizontal axis and vertical axis.
____________________ What is the shape of the histogram?
__________ Based on the relative frequency data, what is the probability of a toss height less than 41 centimeters?
lap time (seconds)
_________ Calculate the sample size n (the number of data pairs) for the data in table two.
______________ Calculate the slope of the linear regression for the table two data. Keep at least THREE non-zero digits in your slope answer!
______________ Calculate the y-intercept of the linear regression for the table two data.
______________ Is the relation positive, negative, or neutral?
______________ Calculate the correlation coefficient r for the data.
______________ Is the correlation none, weak/low, moderate, strong/high, or perfect?
______________ Calculate the coefficient of determination.
______________ What percent in the variation in the height explains the variation in the lap time?
______________ Use the slope and intercept to predict the time for a height of 45 centimeters.
______________ Use the slope and intercept to predict the height to obtain a lap time of 120 seconds.
______________ Even if I could throw a tennis ball zero centimeters high, what would be my lap time predicted by the linear regression?
A smaller lap time is a faster speed, a larger lap time is a slower speed. Based on the strength of the correlation, am I able to control my speed by adjusting the height of my tennis ball tosses as I joggle?