Comparison is made between two measuring instruments, a thermocouple and a flow

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.

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.