Question

5. The frequency distribution below shows the distribution of average seasonal rainfall in San Francisco, as measured in inches, for the years 1967-2017. (SHOW ALL CALCULATIONS FOR B AND C)
(a) Why is it appropriate to use a grouped frequency distribution for this data?
(b) Complete the frequency table with frequency and cumulative relative frequency. Express the cumulative relative frequency to two decimal places.
(c) What percentage of season in this sample has a seasonal rainfall between 0 and 19.99 inches, inclusive?
(d) Which of the following

Season Rainfall (in Inches)	Frequency	Cumulative Relative Frequency
0 - 9.99	1	?
10 - 19.99	22	?
20 - 29.99	?	0.84
30 - 30.99	?	0.98
40 - 40.99	?	1.00
Total	50

Answer 1

a) Since variable "average seasonal rainfall" is continuous, it is appropriate to use a grouped frequency distribution for this data.

b) Consider the following table:

Season Rainfall (in Inches)	Frequency	Cumulative Frequency	Cumulative Relative Frequency
0 - 9.99	1	1	1/50=0.02
10 - 19.99	22	23	23/50=0.46
20 - 29.99	42-23=19	0.84*50=42	0.84
30 - 39.99	49-42=7	0.98*50=49	0.98
40 - 49.99	50-49=1	50	1.00
Total	50

c) From above table (Cumulative Relative Frequency column), 46% of season in this sample has a seasonal rainfall between 0 and 19.99 inches.

d) N/2=50/2=25

The cumulative frequency just greater than 25 is 42. Therefore, median class is 20 - 29.99.