Suppose you have data on the SalePrice of a set of 100 properties.

You calculate the mean and SD of SalePrice, and then the standard units for the 100 properties.
A certain property has standard units +4.

What would you conclude about that property?

Question

Suppose you have data on the SalePrice of a set of 100 properties.

You calculate the mean and SD of SalePrice, and then the standard units for the 100 properties.
A certain property has standard units +4.

What would you conclude about that property?

BlackTom AI · Accepted Answer

We start by understanding what 'standard units' means in this context: converting SalePrice values to z-scores, which express how many standard deviations a value is from the mean. A value with standard units of +4 is four standard deviations above the mean SellPrice, which is far above the typical range of most properties. This extreme position indicates that the property is much more expensive than the bulk of the data, assuming a roughly symmetric distribution where most values cluster around the mean.

Option: "Property X is very expensive, relative to the other properties." This statement aligns with what a +4 z-score implies—being far above the average price—so it accurately describes the relative standing of that property.

Note on potential alternative interpretations: If the distribution of SalePrice were highly skewed, the practical interpretation of a +4 standard unit could vary somewhat, but even in skewed contexts a value four standard deviations above the mean is still unusually high and would be considered very expensive relative to typical properties.

Given the information provided, the conclusion drawn from a z-score of +4 is that Property X is exceptionally expensive compared with the rest of the dataset.

DATA1001/1901 (ND) Evaluate Quiz 3

Suppose you have data on the SalePrice of a set of 100 properties. You calculate the mean and SD of SalePrice, and then the standard units for the 100 properties. A certain property has standard units +4. What would you conclude about that property?

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