# Data Analysis and Presentation

DataAnalysis and Presentation

DATAANALYSIS AND PRESENTATION

Thischapter will present the study finding based on the following themeswith various subthemes being discussed under the main themes. Thethemes will be performing the experiment, statistical analysis ofdata and Conclusion and Recommendation.

Performingthe Experiment

Thisis an experiment which was performed so as to establish whethertemperature and the nature of the surface had any effect on theheight of a bouncing ball. To achieve these two objectives, twoexperiments were carried out.

Descriptionof experiment one

Thefirst experiment was to the effect of temperature on the height of abouncing tennis ball. A general view of a tennis ball has it that, atennis ball is a ball which is made up of a hollow rubber core whichcontains some pressurized hair (Borling, 2012). When this ball fallsto the ground, the hair in the center expands causing the ball tobounce back to the ground. The height of the bouncing ball willdepend on several factors of which it has been presumed thattemperature is one of these factors. In carrying out the experimentpertaining temperature, three identical tennis balls were used. Thefirst tennis ball was heated for twenty minutes the second one wasfrozen for one hour while the third was left at normal roomtemperature. After that had been achieved, the next step was toestablish the height each of the balls was able to bounce. The heatedball was dropped from a 200cm height, and the bounced height was thenrecorded, and a picture was taken. The ball was then dropped for twomore times for the purpose of accuracy. The above procedure was thenrepeated for the other two balls and then the results were recordedand presented as shown below.

AppropriateHypothesis

Vastknowledge in science leads to a number of possible hypothesis. Science has it that, when any object is heated, it expands, due tothis, we can hence conclude that upon heating the bouncing ball, thehair in it will expand (Myers,2006). As a result, the pressure in the ball will increase something whichwill lead to an increase in the bouncing height. On the same, it isbelieved that, once air molecules are heated, the rate of vibrationand interaction increases something which affects the bouncing.Therefore, since there are three conditions which have differenttemperatures, it is presumed that the three conditions will hencemean that the bouncing heights will be different (Stewart, 2015).

Datacollection and Statistical analysis of the Data

Datacollection

Resultsof effects of temperature on bouncing height (cm) of a tennis ball

Table1: Effects of temperature on bouncing height (cm) of a tennis ball

 Trials Heated ball (cm) Frozen ball (cm) Normal ball (cm) 1 107.22 53.31 94.24 2 106.20 53.54 93.30 3 106.34 53.29 92.34 4 106.54 53.29 94.21 5 106.50 53.35 92.35 6 106.68 53.42 93.30 7 107.16 53.41 93.33 8 106.34 53.51 93.26 9 106.33 53.30 93.28 Average (cm) 106.59 53.38 93.29

Imagesshowing the heights of the bouncing tennis balls

Heatedball Frozen ball Normal ball

Source:Practical Work

Statisticalanalysis of the Data

Fromthe information recorded in the table and figures above, it wasevident that temperature does have a lot of effect on the height of abouncing ball. From the data, it was clear that the heated ballbounced to higher heights whose average height was 106.59cm while thefrozen one has the lowest bouncing heights which averaged at 53.38cmwith the ball which bounced at room temperature had a bouncingaverage height of 93.29cm.The pressure inside the ball is said to bethe primary determinant of the height ball bounces. And following thescientific/mathematical equation which determines the pressure ofgas, it is evident that temperature is one of the factors whichaffect the pressure of gas. The equation is “p=rRT” in which ‘p’is the pressure, ‘r’ is the density, ‘R’ is a constant uniqueto the gas and ‘T’ is the temperature (Stewart, 2015). If thedensity of the gas remains constant, a higher temperature will resultin a higher pressure due to their direct proportionality. On theother hand, a decrease in temperature will lead to a reduction inpressure something which will result in a smaller bouncing heightthan that of the fiery ball.

One-wayANOVA: Heated ball (cm), Frozen ball (cm), Normal ball (cm)

Source DF SS MSFP

Factor 2 13803.01 6901.50 35268.73 0.000

Error 244.70 0.20

Total 26 13807.70

S= 0.4424R-Sq = 99.97%R-Sq(adj) = 99.96%

Individual95% CIs For Mean Based on

PooledStDev

LevelN Mean StDev -+-+-+-+

Heatedball (cm) 9 106.590 0.368 *

Frozenball (cm) 953.380 0.096 (*

Normalball (cm) 993.290 0.665 *

-+-+-+-+

60 75 90 105

PooledStDev = 0.442

ANOVAanalysis from MINITAB, the effect of heat is clearly shown. With amean of 106.59, heated ball bounces highest. The difference betweenthe heated ball and the frozen ball is big with a margin of 44.21 cm.

Figure1: Residual Plots for Heated ball (cm), Frozen ball (cm), Normal ball(cm)

Thenormal distribution graph shows the points close to the normalityline. This is a clear indication that it was a random experiment.There is a need to conduct a random experiment to eliminate thechances of having predetermined results.

Figure2: Individual Value Plot of Heated ball (cm), Frozen ball (cm),Normal ball (cm)

Inthe individual value plot above, the effect of temperature on thebounce of a tennis ball is made clear. The heated ball records thehighest bounce with the frozen ball recording the least. Temperature,therefore, clearly affects the extent to whict a tennis ball bounces.When the temperatures increase, the gas molecules inside the tennisball expand. As they expand, it is believed that their energyincreases something which increases their ability to interact andbounce (Harriman, 2012). The increased energy and movement resultsinto a higher bounce (Stewart, 2015). On the other hand, when thetemperatures decrease, the gas molecules contract and move aroundslowly and sluggishly.

Figure3: Boxplot of Heated ball (cm), Frozen ball (cm), Normal ball (cm)

Dueto this, the ball will hence bounce slowly as shown in the boxplotabove.

Descriptionof experiment two

Thesecond experiment was to the effect of the nature of a surface on theheight of a bouncing tennis ball. For this experiment, only one ballis used, but the ball is dropped on two different surfaces. To carryout the test successfully, a measuring ruler is capped and placed ona grass surface and then a ball is dropped from 100cm height to thegrass surface and then the bounce height is recorded following themeasurement of the height using a ruler. To achieve more accurateresults, the ball is dropped two more times for the purpose ofaccuracy. The above procedure is also repeated but, this time, roundusing a hard court surface and then the results are recorded.

Appropriatehypothesis

Thebouncing height of the ball will be less on the grass surface than onthe hard court surface.

DataCollection

Effectsof Nature Surface on the Bouncing Height

Table2 Effectsof Nature Surface on the Bouncing Height

 Trials Grass Surface (cm) Hard Court Surface (cm) 1 42 54 2 43 55 3 42 56 4 42 54 5 43 56 6 42 55 7 43 54 8 43 56 9 42 55

Source:Practical experiment

Statisticalanalysis of the Data

Fromthe data recorded in the table above, it was established that therebound of the ball height was less on the grass surface than on thehard court surface. On average, the bouncing height of the ball ongrass surface was 42.33cm while that of the ball when on the hardcourt surface was 55cm. from the above data, it can be stated thatthe information was so because of the difference in the ability ofthe surfaces to absorb the kinetic energy (Harriman, 2012).

One-wayANOVA: Hard Court Surface (cm) versus Grass Surface (cm)

Source DF SS MS FP

GrassSurface (cm)1 0.450 0.450 0.57 0.476

Error7 5.550 0.793

Total8 6.000

S= 0.8904R-Sq = 7.50%R-Sq(adj) = 0.00%

Individual95% CIs For Mean Based on Pooled StDev

Level N Mean StDev -+-+-+-+

42 5 54.800 0.837 (-*)

43 4 55.250 0.957(–*–)

-+-+-+-+

53.90 54.60 55.30 56.00

PooledStDev = 0.890

TheANOVA analysis from MINITAB compares the means and calculates thestandard deviation. From the ANOVA, it is clear that there is asignificant difference in the bounce of the tennis ball in the twosurfaces.

Figure4: Residual Plots for Hard Court Surface (cm)

Thenormal probability plot above show the residue points being closer tothe normality line. This is a proof that the calculated significancevalue does not differ greatly from the expected significance value.With this in mind, boxplot of hard surface and individual value plotswere developed using MINITAB.

Figure5: Boxplot of Hard Court Surface (cm

Figure6: Individual Value Plot of Hard Court Surface (cm) vs Grass Surface(cm)

Theabove figures show that the tennis ball bounces more on the hardsurface than on the grass surface. This is so because the grasssurface absorbs much of the kinetic energy of the ball meaning thatmore energy will be absorbed when we compare this surface with thehard court surface. Moreover, it has been scientifically proven thatonce a ball is dropped, it dents. The grass surface is in a positionto receive much of the ball denting hence making the bouncing heightto be less. Analysis using Minitab showed that there is a significantdifference in the two surfaces. The normal probability show the plotsbeing close to the normality line. This is an indication of thesignificant difference of the bounce in the two surfaces.

Conclusionand Recommendation

Practicaluseful Overall Conclusion

Fromthe data collected and analysis done, it was established thattemperature and the nature of a surface significantly affect theheight of a bouncing ball. Therefore, it is recommended that for anyactivity which is to be performed using the tennis ball, it isadvisable to use it under certain weather conditions which areapproximately constant or will not cause a significant change in thebouncing height of the ball. Moreover, it is advisable to use theball on a surface which will have an insignificant effect on theamount of kinetic and potential energy so that the ball may notbehave abnormally (Borling, 2012). Also, from the research conducted,the information obtained was found to support my hypothesis thatheated ball will bounce the highest while the frozen ball will bouncethe lowest. The hypothesis of the effect of the nature of a surfaceon the bouncing height of a ball was supported since it wasestablished that the ball bounced on grass surface bounced to asmaller height as compared to when dropped on a hard court surfacedue to the degree of absorption of both the kinetic and the potentialenergy (Goodstein, 2009).

Futurework

Despitehaving to look at the factors which are understood to have an effecton how a tennis ball bounces, it is important to establish whichother factors affects this aspect. Due to this, it is important tocarry out a future study on topics which are related to this subject.Concerning this, I would like to establish whether the age of thetennis ball affects how it bounces. Researchers on severalinstruments have proved that most of these instruments normally dobetter when aged. Due to this, an assumption cannot be just madeconcerning the tennis ball and hence it is important to have anexperiment on the aspect of age.

References

Borling,D. (2012). Historyof the Tennis Ball.Retrieved March 9, 2016, from Who

Inventedthe Tennis Ball?:

Goodstein,M. (2009). Sportscience Projects:The Physics of Balls in Motion.Berkeley Height:

EnslowPublishers.

Harriman,D. (2012). TheTemperature of Tennis Ball.Retrieved March 9, 2016, from

Livestrong:Hobby, N. (2015, December 27). Whatis the effect of Temperature on Tennis Ball.Retrieved March 9, 2016, from Tennis ball:

Myers,R. L. (2006). Thebasics of physics.Greenwood Publishing Group.

Stewart,D. (2015). AScience Project Using Cold Vs. Hot Tennis Balls.Retrieved

March9, 2016, from Aeronautics Internet Textbook: