Question

Mike and Teegan each measured the volume of the 16-ounce bottle three times. They recorded their measurements as shown. Mike: 16.4 oz, 15.2 oz, 15.8 oz Teegan: 16.34 oz, 16.59 oz, 15.13 oz Which statement is true? Mike's measurements are more precise and more accurate. Teegan's measurements are more precise and more accurate. Mike's measurements are more precise, but Teegan's measurements are more accurate. Mike's measurements are more accurate, but Teegan's measurements are more precise.

Answer 1

Answer:

The correct option is;

Mike's measurement are more precise and more accurate

Step-by-step explanation:

The given information are;

The mass of the measured bottle = 16-ounce

The record of the measurements made by Mike are;

16.4 oz

15.2 oz

15.8 oz

The record of the measurements made by Teegan are;

16.34 oz

16.59 oz

15.13 oz

From the two measurements, we have;

The precision of a measurement depends on how close the values of the measurement are to one another, therefore, we have;

For Mike, the precision is given as follows

16.4 - 15.2 = 1.2

16.4 - 15.8 = 0.6

15.8 - 15.2 = 0.6

Total difference = 1.2 + 0.6 + 0.6 = 2.4

For Teegan , the precision is given as follows

16.59 - 16.34 = 0.25

16.59 - 15.13 = 1.46

16.34 - 15.13 = 1.21

Total difference = 0.25 + 1.46 + 1.21 = 2.92

Therefore, Mike's measurements are more precise than Teegan's measurements

The accuracy of the measurement is the amount of closeness the measurements are to a given value

In the question, the given value is 16-ounces of the volume of the bottle

Therefore, by the mean absolute deviation from the 16-ounce of the bottle, we have;

For Mike;

$Mean \ absolute \ deviation = \dfrac{\left | 16.4 - 16 \right | + \left | 15.2 - 16 \right | + \left | 15.8 - 16 \right | }{3} = 0.533$

For Teegan, we have;

$Mean \ absolute \ deviation = \dfrac{\left | 16.34 - 16 \right | + \left | 16.59 - 16 \right | + \left | 15.13 - 16 \right | }{3} = 0.6$

Therefore, Mike's measurement is more accurate than Teegan's measurement.

Which gives;

Mike's measurement are more precise and more accurate.