Question

Water quality ratings (A, B, C, D, F) which reflect the risk of getting sick from swimming at any particular one of 36 Southern California beaches, are given in the following list: A A A F A A A B A C C A A F B A C A D F A D A A D A A D A A A A C F B A (a) (4 marks). Summarize the given ratings by constructing a relative frequency distribution and a bar chart. (b) (2 marks). Assuming that an A means little risk of getting sick, does it appear that the majority of beaches in Southern California are safe? On what information do you base your answer? (c) (2 marks). Would it be appropriate to construct a dotplot for these data? Why or why not?

Answer 1

a) We calculate relative frequency using the formula = frequency/ sum of all frequencies *100

Grade Frequency Rlative frequen 58.33 8.33 21 4 4 4 Total 36 Frequency 10 15 20 25 Frequency

b) Since the relative frequency of A which implies little risk of getting sick is quite high i.e 58.33% it means most of the population is safe. The people with dangers of getting sick are lesser and the majority ie more than 50% belong to rating A and thus are safe.

c)A dot plot can be used here since there are only 5 categories which can be easily represented and the corresponding frequency can be plotted there on.