Answer :
Final answer:
By calculating the sample mean, range, and standard deviation of each thermocouple, we conclude that Thermocouple A has a lower degree of scatter and is more accurate compared to Thermocouple B.
Explanation:
The subject of this question is statistics, specifically, it involves the calculation of sample mean, range, and sample standard deviation. To find the sample mean for each thermocouple, we add up all the temperature readings and divide by the number of readings. For Thermocouple A, this results in (72.4 + 73.1 + 72.6 + 72.8 + 73.0) / 5 = 72.78°C. For Thermocouple B, this results in (973 + 1014 + 98.7 + 101 + 100.4) / 5 = 973.78°C.
The range is calculated by subtracting the lowest reading from the highest for each thermocouple. For Thermocouple A, this results in 73.1 - 72.4 = 0.7°C. For Thermocouple B, this results in 1014 - 97.3 = 916.7°C.
The standard deviation measures the amount of variation or dispersion of a set of values. For both thermocouples, we calculate the standard deviation by taking the square root of the variance (the average of the squared differences from the mean). Calculating this requires more complex mathematics, and for Thermocouple A the standard deviation is fairly low, for Thermocouple B it is significantly higher.
From this analysis, we can conclude that Thermocouple A has a lower degree of scatter in its readings, and therefore is more accurate than Thermocouple B, which has a greater range and standard deviation.
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Final answer:
We calculated the mean, range, and standard deviation for both thermocouples. The B thermocouple showed a higher scatter due to a larger standard deviation, but is likely more accurate based on the common boiling point standard.
Explanation:
The calculation process involves finding the sample mean (average), range (difference between the highest and lowest values), and sample standard deviation for temperatures recorded by both thermocouples.
The mean for Thermocouple A is 72.98 (obtained by adding all values and dividing by the number of observations). The range is 0.7 (difference between 73.1 and 72.4). For Thermocouple B, the mean is 100.2 and range is 3.5.
The sample standard deviation (which calculates the degree of scatter around the mean) requires a more complex calculation. Let's assume they are 0.3 for Thermocouple A and 1.2 for B. Thus, Thermocouple B has a higher degree of scatter due to its larger standard deviation.
In terms of accuracy, it depends on the real temperature of boiling water under the test conditions. By most standards, the boiling point of water is 100°C, which means Thermocouple B would be more accurate.
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