Question

6.1: Math Talk: Differences in Expectations

Mentally calculate how close the estimate is to the actual value using the difference:
actual value-estimated value.
Actual value: 24.8 grams. Estimated value: 19.6 grams
Actual value: $112.11. Estimated value: $109.30
Actual value: 41.5 centimeters. Estimated value: 45.90 centimeters
Actual value: -1.34 degrees Celsius. Estimated value: -2.45 degrees Celsius

Answer 1

To evaluate the accuracy of each estimate in comparison to the actual values, calculate the difference between the actual and estimated values for all examples. The differences obtained are 5.2 grams, $2.81, -4.4 centimeters, and 1.11 degrees Celsius, respectively.

Step-by-step explanation:

To calculate how close an estimate is to the actual value, subtract the estimated value from the actual value. Let's perform these calculations for the examples provided.

• For the actual value of 24.8 grams and an estimated value of 19.6 grams, the difference is 24.8 - 19.6 = 5.2 grams.
• In the case of an actual value of $112.11 and an estimated value of $109.30, the difference is $112.11 - $109.30 = $2.81.
• When the actual value is 41.5 centimeters and the estimated value is 45.90 centimeters, the difference is 41.5 - 45.90 = -4.4 centimeters (negative because the estimate was higher than the actual value).
• Finally, for an actual value of -1.34 degrees Celsius and an estimated value of -2.45 degrees Celsius, the difference is -1.34 - (-2.45) = 1.11 degrees Celsius.

The differences calculated show the deviations from the actual values, demonstrating the accuracy or inaccuracy of the estimations.