creating a Venn diagram from a word problem given - The Cold Be Gone Company conducted a study where 100100100 participants were assigned to either receive a cold medicine or not receive a cold medicine. The Cold Be Gone Company then recorded whether the participant's cold lasted 777 days or longer. The Venn diagram below shows their data. Complete the following two-way frequency table. Received cold medicine Did not receive cold medicine Cold lasted longer than 777 days Cold did not last longer than 777 days A Venn Diagram has 2 overlapping groups, Cold Medicine, 27, and Cold Longer than 7 Days, 20. The overlapping area shared by both groups contains 23. The area not included in any group contains the number 30.

Sahil Khan (last edited 9 months ago)

QUESTION:

ANSWER:

EXPLANATION:

STEP 1: We create a two-way table for the above Venn diagram, based on which the total number of people who received cold medicine was 27+ 23 = 50. Those whose cold lasted longer than 7 days is 23 + 20 = 43. The people who did not participate in any group - or those whose cold did not last longer than 7 days. Those who did not receive cold medicine is 30. Those who received cold medicine and whose cold lasted longer than 7 days is 23. The total number of participants were 100.

STEP 3: Fill in the remaining values.

The total number of people whose cold did not last longer than 7 days is 100 - 43 = 57.

The number of people whose cold did not last longer than 7 days and who received cold medicine is 57 - 30 = 27.

The number of people whose cold lasted longer than 7 days and who did not receive cold medicine is 43 - 23 = 20.

The total number of people who did not receive cold medicine is 20 + 30 = 50.

The above table is the two way frequency table which displays the data in counts.