Question

1. many people travel to the south rim of the grand canyon on vacation each year. the national parks service keeps records of the number of vehicles entering the park. according to their website, the following table lists the total vehicles that entered the park each month from april through september in a recent year.

month # of vehicles
april 127,355
may 140,226
june 135,000
july 145,000
august 175,000
september 128,850
use the table to answer the questions below.

1. add a “relative frequency” column to the table and determine all of the entries in that column. round your entries to the nearest thousandth.
2. add a “cumulative frequency” column to the table and determine all of the entries in that column.
3. add a “relative cumulative frequency” column to the table and determine all of the entries in that column. round your entries to the nearest thousandth.

Explanation:

Step1: Calculate total number of vehicles

$127355 + 140226+135000 + 145000+175000+128850=851431$

Step2: Calculate relative frequencies

April

Relative frequency of April = $\frac{127355}{851431}\approx0.1496$

May

Relative frequency of May = $\frac{140226}{851431}\approx0.1647$

June

Relative frequency of June = $\frac{135000}{851431}\approx0.1586$

July

Relative frequency of July = $\frac{145000}{851431}\approx0.1703$

August

Relative frequency of August = $\frac{175000}{851431}\approx0.2055$

September

Relative frequency of September = $\frac{128850}{851431}\approx0.1513$

Step3: Calculate cumulative frequencies

April

Cumulative frequency of April = $127355$

May

Cumulative frequency of May = $127355 + 140226=267581$

June

Cumulative frequency of June = $267581+135000 = 402581$

July

Cumulative frequency of July = $402581+145000=547581$

August

Cumulative frequency of August = $547581+175000 = 722581$

September

Cumulative frequency of September = $722581+128850=851431$

Step4: Calculate relative cumulative frequencies

April

Relative cumulative frequency of April = $\frac{127355}{851431}\approx0.1496$

May

Relative cumulative frequency of May = $\frac{267581}{851431}\approx0.3143$

June

Relative cumulative frequency of June = $\frac{402581}{851431}\approx0.4728$

July

Relative cumulative frequency of July = $\frac{547581}{851431}\approx0.6431$

August

Relative cumulative frequency of August = $\frac{722581}{851431}\approx0.8487$

September

Relative cumulative frequency of September = $\frac{851431}{851431}=1.000$

Answer:

Month	# of Vehicles	Relative Frequency	Cumulative Frequency	Relative Cumulative Frequency
May	140226	0.165	267581	0.314
June	135000	0.159	402581	0.473
July	145000	0.170	547581	0.643
August	175000	0.206	722581	0.849
September	128850	0.151	851431	1.000