You find an old bathroom scale at a garage sale on your way home from getting a physical exam from your doctor. You step on the scale, and it reads 135 lb. You step off and step back on, and it reads 134 lb. You do this three more times and get readings of 135 lb, 136 lb, and 135 lb. a. What is the precision of this old bathroom scale? Would you consider this adequate precision for the type of measurement you are making? b. The much more carefully constructed and better-maintained scale at the doctor's office reads 126 lb. Assuming that you are wearing the same clothes that you wore when the doctor weighed you, do you think the accuracy of the old bathroom scale is high or low?

a. Precision refers to the consistency of repeated measurements. In this case, the old bathroom scale gave you readings of 135 lb, 134 lb, 135 lb, 136 lb, and 135 lb. The range of these measurements is from 134 lb to 136 lb, so the precision can be considered as ±1 lb. Since the scale consistently gives values within this one-pound range, we would consider it to have adequate precision for general home use, especially considering that body weight naturally fluctuates throughout the day due to various factors like hydration and meals.

b. Accuracy refers to how close a measurement is to the actual or true value. The scale at the doctor's office, which we will assume for this argument is accurate and well-calibrated, read 126 lb. The old bathroom scale shows readings that are consistently higher, around 9 to 10 lb more than the doctor's scale. Therefore, we can conclude that the old bathroom scale has low accuracy.

Extra: When discussing measurements, it's important to understand the difference between precision and accuracy. A measurement is accurate if it is close to the actual value, while it is precise if repeated measurements give very similar results, regardless of how close those results are to the actual value.

For daily activities like monitoring weight at home, a scale with a precision of ±1 lb could be perfectly adequate; however, for medical or professional use, where exact measurements are crucial, a more accurate and precise scale would be necessary.

Also, body weight may not be static throughout the day, as factors like food intake, fluid consumption, and exercise can affect it. Therefore, a slight variation in readings (like the one-pound variation on the old scale) might not be a big concern for most people monitoring their weight at home.

In terms of accuracy, a person might need a more accurate scale for certain medical conditions where tracking small changes in weight is important. Since the old scale consistently overestimates weight by a significant margin (in this case, around 9-10 lb), it would not be suitable for such purposes. It's also worth noting that weighing yourself at the same time of day under the same conditions can help reduce the variability due to these natural fluctuations.