Question

The following frequency distribution shows the number of passengers who flew on a small regional aircraft company’s flight number 1853 for the past 50 days.

Number of passengers on Flight 1853	Frequency (days)	Relative Frequency	Cumulative Relative Frequency
50 to 59	5
60 to 69	13
70 to 79	17
80 to 89	7
90 to 99	6
100 to 109	2

Use this data to construct a relative frequency and cumulative relative frequency distribution. Report all of your answers in the table above to 2 decimal places, using conventional rounding rules.

What percent of the days are there less than 90 passengers on Flight 1853? Report your final answer to 2 decimal places, using conventional rounding rules.

ANSWER:          %

What proportion of the days are there 60 – 69 passengers on Flight 1853? Report your final answer to 2 decimal places, using conventional rounding rules.

ANSWER:         

What percent of the days are there no more than 79 passengers on Flight 1853? Report your final answer to 2 decimal places, using conventional rounding rules.

ANSWER:          %

What is the approximate mean number of passengers on Flight 1853? Report your final answer to 2 decimal places, using conventional rounding rules.

ANSWER:         

What is the approximate variance of the number passengers on Flight 1853? Report your final answer to 2 decimal places, using conventional rounding rules.

ANSWER:         

What is the midpoint of the class interval with the largest frequency? Report your final answer to 2 decimal places, using conventional rounding rules.

ANSWER:         

Answer 1

Relative frequency is the fraction of times an event occurs. So to calculate relative frequency, divide the frequency by total number of days in the sample (that is 50).

Cumulative relative frequency is the accumulation of the previous relative frequencies. Tofind the cumulative relative frequencies,add all the previous relative frequencies to the relative frequency for the current row.

1) For these questions, cumulative relative frequency gives the answer for the percentage value. As an example for the first question,that is,

percent of the days are there less than 90 passengers =

which the cumulative relative frequency directly gives us (multiplying by 100, since tha value is a fraction)

2) Proportion is given directly by relative frequency. So proportion of the days are there 60 – 69 passengers is 0.26

3) percent of the days are there no more than 79 passengers is given by cumulative relative frequency (0.7) that is 70 percent

4) To calculate the mean we use the mid-point of the intervals.

Mean =

           =

           = 74.9

5) variance =

                   = = 163.84

6) Largest frequency is 17 belongin to the interval 70-79.

So mid point of class interval =