This Way and That

Try It

Answer the questions in the following activities. Each item asks you to calculate and interpret joint, marginal and relative frequencies using data in a two-way frequency table. Read each question carefully to identify what frequency is represented by the numerator and which total amount is represented by the denominator in the ratio.

Use the information below to complete the following activity.

Due to a very harsh winter, a local school system has used up all of the allotted snow days. The system’s board of education must decide how to gain back the lost school days. The board proposed various ways and is allowing parents, students and teachers to vote.

The table below shows the proposed ways and the results of the vote.

	Proposals
	Take Away Spring Break	Lengthen the School Day	Lengthen the School Year	Total
Teachers	8	36	1	45
Parents	42	16	22	80
Students	30	43	2	75
Total	80	95	25	200

A two-way table is shown. Three columns are shown, and identified as Proposals. The individual column titles are Take Away Spring Break, Lengthen the School Day, and Lengthen the School Year, respectively. Three rows are shown, each titled teachers, parents, and students. The row entries are 8, 36, and 1 for teachers, 42, 16 and 22 for parents, and 30, 43 and 2 for students. The row totals are provided, which are 45, 80 and 75 respectively. Column totals are also given, which are 80, 95, and 25, respectively.

Use the information below to complete the next activity.

High Marks High School is providing free breakfast during final exam week. In order to offer students the breakfast they most prefer, the teachers survey the students. The following table summarizes the results.

The table below shows the proposed breakfast options and the results of the survey.

	Breakfast Options
	Bagel	Cereal	Fruit	Total
Freshmen	16	74	55	145
Sophomores	23	19	71	113
Juniors	70	4	9	83
Seniors	53	74	48	175
Total	162	171	183	516

A two-way table is shown. Three columns are shown, and identified as Breakfast Options. The individual column titles are Bagel, Cereal, and Fruit. Four rows are shown, each titled Freshmen, Sophomores, Juniors, and Seniors. The row entries are 16, 74, and for Freshman, 23, 19, and 71 for Sophomores, 70, 4, and 9 for Juniors, and 53, 74, and 48 for Seniors. The row totals are provided, which are 145, 113, 83, and 175 respectively. Column totals are also given, which are 162, 171, and 183, respectively.