Question Video: Determining Which Set of Measurements Is More Precise Physics • 9th Grade

A kettle is used to increase the temperature of 0.25 L of water by 50°C, and the time taken for the temperature to change is measured three times. The same kettle is used to increase the temperature of 0.45 L of water by 50°C. Again, three measurements are made. The measured results are shown in the table. Which of the two sets of results is more precise?

02:53

Video Transcript

A kettle is used to increase the temperature of 0.25 liters of water by 50 degrees Celsius, and the time taken for the temperature to change is measured three times. The same kettle is used to increase the temperature of 0.45 liters of water by 50 degrees Celsius. Again, three measurements are made. The measured results are shown in the table. Which of the two sets of results is more precise?

In our table, we see these two volumes of water, each of which was increased in temperature by 50 degrees Celsius. For each volume, the time taken to increase the water’s temperature was measured three times. In this row of our table, we have the three times for the 0.25-liter volume of water, and in the row below it, we have the times for the 0.45-liter volume. We have then two sets of data, and we want to figure out which of these two sets is more precise. Notice that for both instances of heating a volume of water, we’re not given an accurate or a correct amount of time for increasing the temperature of this water by 50 degrees Celsius. Comparing our measured results to that true value would tell us something of the accuracy of our measurements. But here, as we’ve seen, we want to consider their precision.

To know that, we only need to make comparisons among the values of a data set. To see how this will work, let’s clear some space and we’ll write down the values in our two data sets without including their units. To find the precision of a given set of data, we calculate the difference between the greatest value in that set and the least value. That’s one way to express the measurement precision of the set overall. In our first set of data, we see that the greatest value is 15.9. We then subtract from this the smallest value in the set. That’s 15.2. And the result we get, 0.7, is an expression of the precision of this first data set. Let’s now do the same thing for our second set of data. Here, we see that the largest value is 45.4. We subtract from this the smallest value in the set, that’s 44.9, and that difference is equal to 0.5.

Seeing that these two precision indicators are different for the two sets, we might wonder which one shows us which set is more precise. To find that out, let’s imagine a theoretical set of data that is perfectly or completely precise. This would have to be a set where all the values are exactly equal to one another. Let’s imagine a third set of data where all the values in the set are equal to this made-up value of 19.2. We see right away that the difference between the highest and lowest value in this set is zero. This tells us that the more precise a data set is, the closer the difference between the greatest and smallest value in the set is to zero.

Therefore, it’s the smaller of the two calculated precisions we have that indicates the more precise set. This corresponds to our second set of data. So we can write our answer this way. We can say that the measurements of the heating time of the 0.45-liter volume of water, that’s the second data set, are more precise. This then is our answer to “Which of the two sets of results is more precise?”