#1) Does a single outlier have a greater effect on the range or the interquartil
ID: 3042289 • Letter: #
Question
#1) Does a single outlier have a greater effect on the range or the interquartile range? Explain. #2) A vendor measures the weights, in kilograms (kg), of a sample of packages she sends out. The sample mean is 10 kg and the sample standard deviation is 2 kg. The descriptive statistics for this exercise are shown below. Variable Weights Weights*2.2 Weights*2.2 0.1 9 0 22.10 147 4.4014.18 18.91 22.32 26.72 27.16 N N* Mean SE Mean StDev Minimum Q1 Median 9 0 10.000 0.666 2.00 6.400 8.550 10.100 12.100 12.300 9 0 22.00 Q3 Maximum 1.47 4.40 14.08 18.81 22.22 26.62 27.06 She converts the sample mean and sample standard deviation to pounds by multiplying by 2.2. What is the sample mean (in pounds)? What is the standard deviation (in pounds)? How have the mean and standard deviation changed from the original mean and standard deviation? The vendor decides to use a heavier packaging, which increases the weight of each package by 0.1 pounds. Now, what is the sample mean and sample standard deviation (in pounds)? How have the mean and standard deviation changed from the answers in (a)? a) b)Explanation / Answer
1) A single outlier may have a greater effect on range R, (the distance between the lowest and the highest value) than on interquartile range,since an outlier is always an extreme point in a dataset.
However interquartile range (IQR) is one of the commonly used tools for detection of ouliers.
If there exist any point in the dataset below Q1-1.5*IQR and above Q3+1.5*IQR, it may be considered a an outlier.
2)
a) When sample mean and sample standard deviation are converted to pounds, it is multiplied by 2.2.Since, mean and standard deviation are affected by change in scale,
Sample mean (in pounds) = 2.2*Sample mean
= 22 pounds
Standard deviation (in pounds) = 2.2*2
= 4.4 pounds
The mean and standard deviation has changed 2.2 times from the original.
b)Now since mean is affected by change in origin, increaing the weight of each package by 0.1 increases the mean by 0.1
sample mean (in pounds) = 22+0.1
= 22.1 pounds
The standard deviation is independent of origin.Hence,
Standard deviation = 4.4 pounds
From the case in a),the mean has incresed by 0.1 pounds,while there is no difference in it's Standard deviation
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