Question Video: Identifying the Usefulness of Repeated Measurements | Nagwa Question Video: Identifying the Usefulness of Repeated Measurements | Nagwa

# Question Video: Identifying the Usefulness of Repeated Measurements Physics

When taking any measurement, why is it recommended to take the measurement several times and then calculate the average of the readings? [A] To increase the precision of the measurement. [B] To reduce the effect of the errors in the individual readings. [C] To eliminate any measurement errors in the individual readings. [D] Because the average of the readings is the real value of the measurement.

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### Video Transcript

When taking any measurement, why is it recommended to take the measurement several times and then calculate the average of the readings? (A) To increase the precision of the measurement. (B) To reduce the effect of the errors in the individual readings. (C) To eliminate any measurement errors in the individual readings. (D) Because the average of the readings is the real value of the measurement.

Let’s consider these answer options in turn, beginning with option (A). We know that the precision of a measurement has to do with the uncertainty of the device used to make that measurement. For example, a ruler that was marked out to the nearest millimeter would give more precise measurements of length than a ruler marked out to the nearest centimeter. Measurement precision then doesn’t have to do with how many measurements are made. For this reason, we won’t choose option (A) as an explanation for why when making any measurement, it’s recommended to take several measurements and calculate their average.

Option (B) says that the reason for doing this is to reduce the effect of the errors in the individual readings. This does make sense. Let’s say, for example, that we’re making measurements of some quantity, where the actual value of that quantity is 15. If we made just one measurement of that value, due to errors, we might get a result different from the actual value. We might, for example, have a random error occur and measure a value of 17 instead of what we should get of 15. If we collect all of our measured values and calculate their average, then we get a value closer to the actual value, in this case exactly equal to that actual value. Averaging the results then has indeed reduced the effect of errors in the individual readings. Answer choice (B) is looking like it will be our final answer.

But just to make sure, let’s consider options (C) and (D). Option (C) says that making multiple measurements and calculating their average will eliminate any measurement errors in the individual readings. In general though, this is not the case. Considering our imaginary measured set of data, let’s say that instead of a value of 17, on this trial, we had recorded a value of 18. That would mean then that the average of these five measured values is no longer exactly 15, the actual value. Therefore, this process of making multiple measurements and averaging out those measurements doesn’t eliminate measurement errors that are made. Rather, as option (B) says, it reduces their effect. We won’t choose then answer choice (C).

And considering answer option (D), we can actually imagine a case as we see here, where the average of the measured values of a quantity is not exactly equal to the true value of that quantity. Indeed, it’s generally the case that the average of a series of measured values is not equal to the real value of the quantity being measured. We see that answer option (B) is indeed our final choice.

When making a measurement, it is recommended to take the measurement several times and then calculate the average of the readings in order to reduce the effect of the errors in the individual readings.

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