Comparison is made between two measuring instruments, a thermocouple and a flow
ID: 707673 • Letter: C
Question
Comparison is made between two measuring instruments, a thermocouple and a flow meter. The thermocouple measures temperature in °C while the flow meter measures flow rate in liter per second. The data below shows five measurements of each instrument TC)-Thermocouple 1244 100790,7 0.08 128.1 126.6 0.078 130.5 0.075 122.8 | V (L/s)--Flow meter 0,082 (a) For each instrument, calculate the sample mean, range, and the standard deviation (b) Which thermocouple is more accurate? Explain your answer. (c) If a n instrument is considered defective for a measured data that exceeds two standard deviation of the mean value, which of the thermocouple will be considered defective. Explain your answer.Explanation / Answer
1. Range is the difference between highest and lowest data in a set.
mean can be calculated as sum of all the values/ total number of values.
standard deviation is squareroot of ((xi-x)2/n) where xi is data, x is mean and n is total no. data points.
for thermocouple - range = 130.5 - 122.8 = 7.7
mean = (124.4 + 128.1 + 126.6 + 122.8 + 130.5)/5 = 126.48 ~ 126.5
standard deviation = (((124.4-126.5)2 + (128.1-126.5)2 + (126.6-126.5)2 + (122.8-126.5 )2+ (130.5-126.5)2)/5)1/2 = 2.70
every value is in celsius.
for flowmeter -- range = 0.082 - 0.075 = 0.007
mean =( 0.082 + 0.079 + 0.08 + 0.078 + 0.075)/5 = 0.0788
standard deviation using similar formula is = 0.0023.
readings in l/s
2. The thermocouple measuring 126.6 is more accurate as it much more closer to the mean value that is 126.48.
3. 2*standard deviation for thermocouple data = 2.70*2 = 5.4
deviation for different thermocouple = |124.4 - 126.5| = 2.1
|128.1 - 126.5| = 1.6
|126.6 - 126.5| = 0.1
|122.8 - 126.5| = 3.7
|130.5- 126.5| = 4
As no value is greater than 5.4 no thermocouple is considered defective.
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