Measurements and Statistics

1. A certain physics lab instructor buys two bathroom scales at a garage sale to help launch his diet.  Within a five minute time span, he weighs himself four times each on each scale (i.e., his true weight does not change). Stepping on it four different times, scale A gives the following four readings in kg:

Scale A:  192, 191, 193, 193 kg

Scale B gives four different readings:

Scale B: 192, 208, 199, 204 kg

He then immediately goes to use the fancy scale at the SVC gym to get an accurate value, which is 201 kg.

Which of the following is the best answer (pick only one):

• Scale B has a random error problem only
• Scale A has a systematic and random error problem
• Scale B has a random and systematic error problem
• Scale A has a random error problem only
• Whoa. Why is this bubba weighing himself instead of working out at the gym?

2. What is the standard deviation of the Scale B data? Recall Scale B measurements were 192, 208, 199, and 204 kg.  (no units required)

3. What is the standard deviation of the Scale A measurements?  Recall the Scale A measurements are 191, 192, 193 and 193 kg. (no units required)

4. Two lab groups collect measurements of the length of an iron-titanium rod. Group A's measurements are 16.7 cm, 17.3 cm, and 17.1 cm.  Group B's measurements are 14.8 cm, 19.0 cm, and 16.9 cm.  The professor's measurement (the "true" value) is 16.87 cm. Which of the following is the best statement (pick only one please):

• Group B is the most accurate but least precise
• Group A is the most accurate but least precise
• Group B is the most accurate and most precise
• Group A is the most accurate and most precise
• Group A watches too much TV

5. Based on your reading and your response to the questions above, which of the following is the best statement?  Pick only one, please.

• Standard deviation is an indicator of the precision of a set of measurements
• Standard deviation is an indicator of the accuracy of a set of measurements
• Standard deviation is an indicator of both the accuracy and precision of a set of measurements
• Standard deviation doesn't tell us anything about accuracy or precision
• Standard deviation is a formula with funky Greek letters and is quite confusing to me