Video: Interpreting Data in a Scatterplot

A medical examiner in a school created the given scatterplot to examine the relationship between the heights and weights of nine different students. Which of the labeled points represents the student with the greatest weight-to-height ratio?

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Video Transcript

A medical examiner in a school created the given scatterplot to examine the relationship between the heights and weights of nine different students. Which of the labeled points represents the student with the greatest weight-to-height ratio?

The location along the 𝑥-axis will give us the height of these students. And the location along the 𝑦-axis will give us the weight of the students. And we need to calculate weight-to-height ratios for the points labeled 𝐴, 𝐵, 𝐶, and 𝐷. First, we’ll consider these ratios in fraction form, with the weight as the numerator and the height as the denominator. Let’s start with student 𝐴. The weight is 80 kilograms. And the height falls a little bit less than halfway between 155 and 160. So we could say it’s about 157 centimeters. And the weight-to-height ratio for student 𝐴 is 80 over 157.

We follow the same procedure for student 𝐵. The weight here, 85 kilograms. The height would fall a little bit less than halfway between 175 and 180, but slightly closer to 175. And so we could call it 176. Now, student 𝐶 has a weight of 75 kilograms and a height that is just a bit more than 170 centimeters. And so we’ll say 171 centimeters. And finally, option 𝐷 is a student with the weight of 90 kilograms and a height that is exactly halfway between 185 centimeters and 190 centimeters, which would be 187 and a half, 187.5.

Now, the student with the greatest weight-to-height ratio is not the student that has the greatest weight. We have to be careful when we try to compare these ratios. We don’t just look at the numerator, because each of these fractions, each of these ratios, have a different denominator. If we wanted to compare them as fractions, we would have to find a common denominator. And since these numbers are so large, it’s not an easy task to find a common denominator for these four values.

Instead, we can compare by converting these fractions into decimals. We do this by dividing the numerator by the denominator. 80 divided by 157 equals 0.5095 continuing. 85 divided by 176 equals 0.4829 continuing. 75 divided by 171 equals 0.4385 continuing. And 90 divided by 187.5 is exactly 0.48. Since we’re looking for the greatest weight-to-height ratio, we’re interested in the largest decimal value. 0.5095 continuing is the greatest decimal value. It has a five in the tenths place. The other three ratios have a four in the tenths place.

Since student 𝐴 has the highest decimal value, 80 over 157 is the greatest weight-to-height ratio of the four labeled points. It means that student 𝐴 has the greatest weight-to-height ratio of the four labeled points.

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