# I don't understand which would be the outlier.They all seem to be outliers to me. Thanks!The 5 number summary for the average daily temperature in Atlantic City, NJ (given in Fahrenheit) is 31, 39,...

I don't understand which would be the outlier.They all seem to be outliers to me. Thanks!

The 5 number summary for the average daily temperature in Atlantic City, NJ (given in Fahrenheit) is 31, 39, 52, 68,76. Draw the box-and-whisker plot for this data and use it to determine which of the following would be considered an outlier if it were included in the data.

(a) January’s record high temperature of 78◦.

(b) January’s record low temperature of −8◦.

(c) April’s record high temperature of 94◦.

(d) The all time record high of 106◦.

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### 1 Answer

We are given the five number summary for a set of data: 31,39,52,68,76.

(1) The definition of an outlier varies by text. In a typical first course in statistics, you might see the definition as any point that is `+-1.5(IQR)` (IQR is the inter-quartile range) from `Q_3,Q_1` respectively. In other words, a point that is 1.5*IQR above Q3, or 1.5*IQR below Q1.

There are a number of other definitions, many based on other statistical measures.

(2) Using the definition given above, we can compute the inter-quartile range. `IQR=Q_3-Q_1=68-39=29` . So 1.5*IQR=43.5.

Any point 43.5 units below `Q_1=39` or 43.5 units above `Q_3=68` would be deemed an outlier.

**Thus a point below 39-43.5=-4.5 would be an outlier. Thus (b) would be an outlier.**

Also, any point above 68+43.5=111.5 would be an outlier. There are no data entries above this value.

** Note that an outlier should lie significantly away from the median -- many definitions merely suggest ways of assigning probabilities to whether a datum is an outlier. Depending on the context, an outlier might suggest an error (keying data incorrectly, poor measurement, etc...) or a faulty model, or other causes.

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