64 Group A: Group B: Question 4- The first set (Group A) is the same as discusse

Question

64 Group A: Group B: Question 4- The first set (Group A) is the same as discussed above. The second set of data are from another group of students (Group B) who also rolled the ball from the same height. What do you notice between the two sets of data? Although the average of the two data sets is actually the same (653.6 mm), the data fromm group A are spread over a larger range than the data from group B. Which group do you think did a more careful experiment? A careful experiment leads to better data. We usually say that the better data are of a higher quality. Clearly the quality of the data from Group B is better than the quality of the data of Group A since the spread is smaller in B than for A. We therefore need some way of quantifying the spread of data points about the mean R or uncertainty in the observed readings The size of the spread can be quantified by the value that is called standard deviation, . It measures the amount of variation or dispersion from the average. The larger a standard deviation, the larger an uncertainty of the measurements. The standard deviation is defined the way so about 2/3 (60%) of data points are within the range from R- to Rave+ (see the figure). Standard Deviation is about 10 cm Average 65.4cm 62 64 65 63

Explanation / Answer

4). As the data points from group B are less scattered, it means they were very carefull while taking readings and most of the reading had least standard deviation and hence least uncertainity. We can easily predict a trend between those data points whereas it will be difficult in case of group A.

Also the relative uncertainity is also the least in group B.

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