heieae the Bellowing sample of TN (total mitregen) loads (kg N/day) from ty loca
ID: 3374952 • Letter: H
Question
heieae the Bellowing sample of TN (total mitregen) loads (kg N/day) from ty location, displayed here in increasing order 1709 18.12 23.70 24.07 55.02 57.00 5841 61.31 106.80 108.69 114.61 1 35.07-19599-140.32 142.51 61.3164.25 30.75 49.98 66.14 103.61 143.75 149.64 167.79 182.50 31245 352.09 371.47 444.68 152935 30,??13154- 5.0736.99 i5006 issa2 | 67.68 81.40 90.80 92.17 92.42 1008 120.86 124.54 193.53271.57 563.92 690.11 Find he media(lower quartile(, upper quartile (02, and inter quartile range C the datasct b. Identify any mild outliers. c. Identify any extreme outliersExplanation / Answer
The data is already sorted.
Let the data be represented by x1 = 9.69 to x57 = 1529.35.
So, the median will be given by Q2 = x29 = 92.17.
The first quartile = Q1 = median of first half = (x14+x15)/2 = (42.51 + 45.64) / 2 = 44.075.
The third quartile = Q3 = median of second half = (x43+x44)/2 = (167.79 + 182.50) / 2 = 175.145.
So, the inter quartile range = IQR = Q3 - Q1 = 175.145 - 44.075 = 131.07.
b. The outliers are identified by values which are less than 1.5 times IQR from quartile 1 or greater than 1.5 times IQR from quartile 3.
On the lower side, outliers will be less than Q1-1.5*IQR = 44.075 - 1.5 * 131.07 = -152.53. As there are no negative values, there are no outliers on the lower side.
On the upper side, outliers will be greater than Q3+1.5*IQR = 175.145 + 1.5 * 131.07 = 371.75. So, the values greater than 371.75 will be classified as outliers.
Of these outliers, values which are within 3 times IQR are further classified as mild outliers.
As there are no outliers on the lower side, there are also no mild outliers on that side.
On the upper side, mild outliers will be less than Q3+3*IQR = 175.145 + 3 * 131.07 = 568.355. So, all the values in the range (371.75, 568.355) are mild outliers. Looking at the data, we see that mild outliers = 444.68, 460.86, 563.92.
c. The extreme outliers are identified by values which are less than 3 times IQR from quartile 1 or greater than 3 times IQR from quartile 3.
As there are no outliers on the lower side, there are also no extreme outliers on that side.
On the upper side, extreme outliers will be greater than Q3+3*IQR = 175.145 + 3 * 131.07 = 568.355. So, values which are greater than 568.355 will be classified as extreme outliers. Looking at the data, we see that extreme outliers = 690.11, 826.XX, 1529.35.
(Note the second last value is not completely visible. Please use that value in the above statement instead of 826.XX.)
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