Question

9) A temperature control system is designed to maintain the temperature at a constant value of 500°C inside an induction furnace.

a) The following test set of initial temperature measurements (once the furnace has temperature has reached steady state) is obtained: 507 502 520 500 492 485 499 495 497 500 516 501 489 503 490 481 504 511 499 512
Show that this is free of rogue data points and can therefore be used as a reference set against which to test future temperature measurements.
b) The temperature is then measured at 10 min intervals and the following 20 measurements were obtained: 481 505 495 519 498 1015 508 477 500 526 501 488 502 492 464 503 499 510 515 497
Test wheter there are any rogue measurements in this data set.

Answer 1

a) For the first data,

The first quartile is 494.25 and the 3rd quartile is 504.75. So, IQR = 10.5.

So, using the formula (Q1 - 1.5*IQR, Q3 + 1.5*IQR), we have the interval (478.5, 520.5).

If there is an observation outside of this interval then there will be a rough value/outlier. But the minimum and the maximum value of the data is 481 and 520, respectively. So, there are no outliers.

b) Now for this data,

The first quartile is 494.25 and the 3rd quartile is 508.5. So, IQR = 14.25.

So, using the formula (Q1 - 1.5*IQR, Q3 + 1.5*IQR), we have the interval (472.875, 529.875 ).

But, the minimum and the maximum value of the data is 464 and 1015, respectively. So, some observations are outside of the interval. So, there are some rough data points or outliers and the data point is 1015.