Question

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 work. Not Just the answer.)

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

(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 seasonal rainfall groups does the median of this distribution belong to? 10-19.99, 20 – 29.99, or 30 – 39.99? Why?

Answer 1

(a) Grouped data are formed by aggregating individual observations of a variable into groups, so that a frequency distribution of these groups serves as a convenient means of summarising or analysing the data. A grouped frequency distribution is an ordered listed of a variable X, into groups in one column with a listing in a second column, the frequency column. A grouped frequency distribution is an arrangement class intervals and corresponding frequencies in a table. It is very useful when the scores have many different values.Grouped frequency distribution helps to organize the data more clearly. It is more useful when the scores have multiple values. List of average seasonal rainfall in San Francisco, as measured in inches, for the years 1967-2017 contains many different values. So it is required to construct  grouped frequency distribution for this data for analysing the data.

(c) The percentage of season in this sample has a seasonal rainfall between 0 and 19.99 inches=0.46x100=46%.

(d) N=50, N/2=25

Now 23<25<42 hence the median belongs to the class whose corresponding cumulative frequency is 42.

Hence the median class=20 – 29.99