Envision Math 2.0: Grade 8, Volume 1
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5. Interpret Two-Way Relative Frequency Tables
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Exercise 12 Page 242

Practice makes perfect

We are asked to complete the following sentence based on the relative frequencies presented in the column two-way relative frequency table.

A greater percent of people given saw an improvement.

Let's take a look at the given table. We know that patients were given either Medicine A or Medicine B. Then they were asked about their improvement.
Improvement?
Type Yes No Total
Medicine A 26 % 64 % 50 %
Medicine B 74 % 36 % 50 %
Total 100 % 100 % 100 %

We should compare the share of Yes responses to determine for which medicine a greater percent of people saw an improvement. Let's highlight these values.

Improvement?
Type Yes No Total
Medicine A 26 % 64 % 50 %
Medicine B 74 % 36 % 50 %
Total 100 % 100 % 100 %

Among the patients who saw an improvement, only 26 % of them were given Medicine A, while 74 % got Medicine B. 26 %& < 74 % Medicine A & < Medicine B This means that the majority of patients that saw an improvement were given Medicine B. We can now complete the sentence.

A greater percent of people given Medicine B saw an improvement.

We want to determine if there is evidence that improvement was related to the type of medicine. To do this, let's take a look at the column representing Yes responses.
Improvement?
Type Yes No Total
Medicine A 26 % 64 % 50 %
Medicine B 74 % 36 % 50 %
Total 100 % 100 % 100 %

We can see that about three quarters of the respondents that saw the improvement were given Medicine B. On the other hand the majority of patients that did not see the improvement were given Medicine A. This can be seen as evidence that improvement is related to the type of medicine.