Consider the following set of replicate measurements: 36.61 35.37 35.43 35.28 34
ID: 497184 • Letter: C
Question
Consider the following set of replicate measurements: 36.61 35.37 35.43 35.28 34.94 a) Apply the Q lest to this set to determine if one of the values should be discard, tor fi' observations the value of Q is 0.64 at the 90% confidence value. Do you keep or discard the outlier? Keep ____, Discard ____ After you perform the Q test answer the following questions: b) calculate the mean mean = ___ c) calculate the median median = ____ d) calculate the average deviation from the mean average deviation = ____ e) report the answer with correct significant figures and error (+/-) reported value = ____ +/- ____Explanation / Answer
a) The N values comprising the set of observations under examination are arranged in ascending order:
34.94, 35.28, 35.37, 35.43, 36.61
Now calculate Q -
Q = X2 – X1 /Xn –X1
Q = 35.28 – 34.94/ 36.61 - 34.94
Q = 0.34 /1.67 = 0.203
We discard observation 36.61 as an outlier at a 90% confidence level
The corresponding Qexp = 0.20. Qexp is less than Qcrit value (= 0.64 at CL 90% for N=5).
b) The mean is the usual average, so add all set of data including outlier and then divide by N
(34.94 + 35.28 + 35.37 + 35.43 + 36.61) /5 = 35.53
Mean = 35.53
c) Median-
The median is the middle value, which is not affected by outliers.
Median- 35.37
d) Average deviation from mean
Mean = 35.53
Find the distance of each value from that mean-No minus signs
34.94 – 35.53 = 0.59
35.28 – 35.53 = 0.25
35.37 - 35.53 = 0.16
35.43 – 35.53 = 0.10
36.61 – 35.53 = 1.08
Add up all of the values and divide by N
Average deviation = (0.59 + 0.25 + 0.16 + 0.10 + 1.08)/5
= 0.436
e) Correct significant figure = 0.44