# MS 150 Statistics midterm • Name:

Throws
183
177
186
183
189
204
198
196
178
205

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.

1. _________ What level of measurement is the data?
2. __________ Calculate the sample size n for the data.
3. __________ Determine the minimum.
4. __________ Determine the maximum.
5. __________ Calculate the range.
6. __________ Calculate the midrange.
7. __________ Determine the mode.
8. __________ Determine the median.
9. __________ Calculate the sample mean x.
10. 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]
11. __________ Calculate the sample coefficient of variation CV.
12. __________ If this data were to be divided into four classes, what would be the width of a single class?
13. 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:
14. Sketch a frequency histogram chart of the data anywhere it fits, labeling your horizontal axis and vertical axis as appropriate.
15. ____________________ What is the shape of the distribution?
16. __________ 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.
17. ____________________ Is the z-score for 178 an ordinary or unusual z-score?
18. __________ 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.
19. ____________________ 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
2.5189
2.5198
2.6196
2.0178
2.9205
1. __________ Calculate the slope of the linear regression for the data.
2. __________ Calculate the y-intercept of the linear regression for the data.
3. __________ Use the slope and intercept to predict the number of throws for a lap of 2.3 minutes.
4. __________ Use the slope and intercept to predict the time for a lap with 185 throws.
5. __________ Does the relationship appear to be linear, non-linear, or random?
6. __________ Is the correlation positive, negative, or neutral?
7. __________ Calculate the correlation coefficient r.
8. __________ What is the strength of the correlation: strong, moderate, weak, or none?
9. __________ Calculate the coefficient of determination r².
10. __________ What percent of the variation in the lap time in minutes explains the variation in the number of throws?
11. 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?