Answer :
Final answer:
We can estimate the uncertainty in these measurements by calculating the standard deviation of the weights. We can estimate the bias as the scale's reading when no one is standing on it, which is 2lbs. Both uncertainty and bias can thus be accounted for in these measurements.
Explanation:
In the study of physics, we can estimate the uncertainty and bias in these measurements. The uncertainty in a measurement depends on the measuring device and could be estimated by calculating the standard deviation of the measurements: (152, 151, 150, 148). The bias is a systematic (built-in) error in measurement that makes all values skewed in one direction from the true value, and it can be estimated by taking the reading of the scale when the person is not on it (2 lbs in your case). The bias then can be subtracted from each recorded weight.
The difference between 1 and 2 units of weight is likely going to be more reliably detectable than a difference between 20 and 21 units because uncertainty in measurement depends on the precision of the measuring instrument used.
Therefore, yes, we can estimate both the uncertainty and bias in these measurements under the chosen condition.
Learn more about Measurement Uncertainty and Bias here:
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The uncertainty in the measurements, which is approximately 1.35 pounds, but without additional information or calibration, we cannot estimate the exact bias in these measurements.
1. Uncertainty:
To estimate the uncertainty in the measurements, we can calculate the standard deviation of the readings.
The four readings are 148, 151, 150, and 152. We can calculate the mean by summing the readings and dividing by the number of readings:
Mean = (148 + 151 + 150 + 152) / 4 = 150.25 pounds.
Next, we calculate the differences between each reading and the mean:
Differences: -2.25, 0.75, -0.25, 1.75
To calculate the standard deviation, we need to square each difference, sum the squared differences, divide by the number of readings, and take the square root:
Standard Deviation = √(((-2.25)² + 0.75² + (-0.25)² + 1.75²) / 4) ≈ 1.47 pounds.
Therefore, the estimated uncertainty in these measurements is approximately 1.47 pounds.
2. Bias:
Bias refers to a consistent deviation from the true value.
In this case, it's not possible to estimate the bias with only the given information.
To estimate the bias, we would need a reference value or another independent measurement to compare the readings against. Without such information, we cannot determine if the readings are consistently higher or lower than the true weight.
To learn more about the standard deviation;
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