Which one(s) of these twelve brands would be considered outliers, if there are indeed any at all? How extreme does something have to be considered an outlier?
Brand,Strawberry,Vanilla
1,140,140
2,210,230
3,200,170
4,200,180
5,110,100
6,180,180
7,210,150
8,140,150
9,150,150
10,220,220
11,110,120
12,210,210
google will give lots of references.
wikipedia has a good article, but some of it is hard going.
wolframalpha.com also has a nice article at
http://mathworld.wolfram.com/Outlier.html
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To determine if there are any outliers among the given brands, we can use a common method called the Tukey's fences method. According to this method, any data point outside the range of 1.5 times the interquartile range (IQR) below the lower quartile (Q1) or above the upper quartile (Q3) can be considered an outlier.
First, let's calculate Q1, Q3, and the IQR for both the Strawberry and Vanilla columns:
Strawberry:
Q1 = 140
Q3 = 210
IQR = Q3 - Q1 = 210 - 140 = 70
Vanilla:
Q1 = 150
Q3 = 210
IQR = Q3 - Q1 = 210 - 150 = 60
Now, we can calculate the lower and upper fences for both columns:
Lower fence (Strawberry) = Q1 - 1.5 * IQR = 140 - 1.5 * 70 = 35
Upper fence (Strawberry) = Q3 + 1.5 * IQR = 210 + 1.5 * 70 = 385
Lower fence (Vanilla) = Q1 - 1.5 * IQR = 150 - 1.5 * 60 = 60
Upper fence (Vanilla) = Q3 + 1.5 * IQR = 210 + 1.5 * 60 = 300
Now let's compare the values of each brand in both columns to the respective fences:
Brand 1: Strawberry = 140, Vanilla = 140 (within the fence)
Brand 2: Strawberry = 210, Vanilla = 230 (within the fence)
Brand 3: Strawberry = 200, Vanilla = 170 (within the fence)
Brand 4: Strawberry = 200, Vanilla = 180 (within the fence)
Brand 5: Strawberry = 110, Vanilla = 100 (within the fence)
Brand 6: Strawberry = 180, Vanilla = 180 (within the fence)
Brand 7: Strawberry = 210, Vanilla = 150 (within the fence)
Brand 8: Strawberry = 140, Vanilla = 150 (within the fence)
Brand 9: Strawberry = 150, Vanilla = 150 (within the fence)
Brand 10: Strawberry = 220, Vanilla = 220 (within the fence)
Brand 11: Strawberry = 110, Vanilla = 120 (within the fence)
Brand 12: Strawberry = 210, Vanilla = 210 (within the fence)
Based on the calculations, there are no outliers among the given brands for either the Strawberry or Vanilla columns. Remember that outliers are considered extreme values that fall outside the calculated fences, which are 1.5 times the IQR below Q1 or above Q3.