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Chapter 2: Problem 58

Three people measure the distance from Main Street to Market Avenue using their best estimates. Their data are \(2.5\) miles, \(2.5\) miles, and \(2.6\) miles. Survey charts show the actual distance to be \(1.8\) miles. Characterize the collected data in terms of accuracy and precision.

Short Answer

Expert verified
The collected data is characterized by low accuracy, as the mean of the estimated distances is 0.733 miles away from the actual distance of 1.8 miles. However, the data has high precision, as the differences between the estimated distances are very small (0.1 miles or less).

Step by step solution

01

Calculate the mean of the estimated distances.

To calculate the mean, sum up the three given distances and divide the result by the number of measurements. Mean = \(\frac{2.5 + 2.5 + 2.6}{3} = \frac{7.6}{3} = 2.533\) miles
02

Compare the mean to the actual distance to determine the accuracy.

The actual distance is given as 1.8 miles. We can find the absolute difference between the mean and the actual distance: Difference = \(|2.533 - 1.8| = 0.733\) miles This difference indicates that the estimated distances are not very accurate as they are quite far from the actual distance of 1.8 miles.
03

Analyze the variation of estimated distances to determine the precision.

Observe the three evaluated distances: 1. 2.5 miles 2. 2.5 miles 3. 2.6 miles All the evaluated distances are very close to each other. The differences among these measured values are only 0.1 miles or less, which makes them precise.
04

Characterize the collected data.

Based on our analysis, we can characterize the collected data as follows: - The data have low accuracy since the mean of the estimated distances is far from the actual distance (0.733 miles away). - The data have high precision since the differences among the estimated distances are very small (0.1 miles or less).

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