# During gym class, four students decided to see if they could beat the norm of 45 sit-ups in an hour. The first student did 64-sit-ups, the second did 69, the third did 65, and the fourth did 67. Is...

During gym class, four students decided to see if they could beat the norm of 45 sit-ups in an hour. The first student did 64-sit-ups, the second did 69, the third did 65, and the fourth did 67. Is this information accurate, precise, both or neither?

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Accuracy and precision are words used to describe measurements. Accuracy describes the closeness to a known or accepted value/measurement while precision refers to the closeness of repeated measurements.

If we look at the data given (norm of 45 sit-ups and experimental data of 64, 69, 65, and 67 sit-ups) out of any context, then we would say that the experiments were not accurate (as they deviate substantially from the accepted value) but that they were relatively precise as the repeated experiments had about the same value.

If your refrigerator was known to be set at 35 degrees F, but a thermometer measures the temperature at 42 degrees, then the thermometer is not accurate (perhaps it was not calibrated correctly). If you repeated the measurements and got results of 41, 42, 41, 43, 40 then the measurements are precise, but not accurate.

If, on the other hand, you got readings of 32, 35, 36, 34, 34, 37 then your measurements are accurate (close to 35) but not very precise.

Another example is shooting at a target: a tight cluster represents precision (even if you are off center), many shots in the center are accurate (even if spread out), while a tight cluster in the center is accurate and precise, and shots spread all over the target are neither accurate nor precise.

There are a number of things wrong with the problem as stated. We are given a "norm" (mean, median, mode?) of 45 situps per hour. The experimental data does not give a time, so perhaps we are comparing different things so the data would not be accurate, because we do not know the expected value.

We aren't really repeating the experiment, as different people are doing the sit-ups. I would imagine that an athletic team might do better than the general public, and individual abilities will vary, so we cannot measure the precision. If we took the average of the four boys results we could compare that average to the "norm" and decide that it was not accurate (perhaps because of additional time given or allowing "cheats") but then we have only one comparison so we cannot discuss the precision. The boys would have to repeat the experiment and compare the averages of each trial to check for precision.