Question

I am thinking this question is asking about nominal, ordinal, interval and ratio. not sure how to answer second part?

State which type of measurement scale each represents, and then which center measures can be use for the variable?

1. You collect data on the height of plants using a new fertilizer.
2. You collect data on the cars that people drive in Campbelltown, Australia.
3. You collect data on the temperature at different locations in Antarctica.
4. You collect data on the first, second, and third winner in a beer competition.

Answer 1

data on the height of plants using a new fertilizer

Height is a variable which can be measured by numbers and for which we know the order as well the exact differences between the values. Also, an absolute zero exists. So, the height of plants is Ratio scale of measurement.

Median is the center measure that can be used for height of plants. Due to the effect of a fertilizer, the height of plants normally take values close to a central value. But there can be some plants whose height are abnormally low or abnormally high, resulting in presence of outliers. In such a case, median is the appropriate measure of central tendency, since it remains unaffected by the presence of outliers.

data on the cars that people drive in Campbelltown, Australia

Cars is an attribute, so it cannot be measured in numbers. Also, there is no order for cars, only different cars are seen. So, the cars is Nominal scale of measurement.

Mode is the center measure that can be used for cars. The cars that people drive in Campbelltown, Australia, are observed and the car which appears the most on road must be the car which people normally buy. This implies that the car which has the highest frequency represents the center car. Also, cars being an attribute, cannot have any mean or median value. The best that can be done is indicating which car was the most frequent. So, mode is the appropriate measure of central tendency.

data on the temperature at different locations in Antarctica

Temperature is a variable which can be measured by numbers and for which we know the order as well the exact differences between the values. But there is no absolute zero. So, the temperature at different locations is Interval scale of measurement.

Mean is the center measure that can be used for temperature. Mean is normally the most appropriate center measure in case of a variable, except the case where some extreme values or outliers are present. In this case, as all the locations are in Antarctica, there are no outliers and all the values of temperatures at different locations are around the arithmetic mean temperature. So, mean is the appropriate measure of central tendency.

data on the first, second, and third winner in a beer competition

This data only has a inherent order but no numerical measurements. So this data is Ordinal scale of measurement. But if the data is considered as the amount of beer drunk by the contestants, there is not only a inherent order but also numerical measurements of the amount of beer drunk which has an absolute zero. In such a case, this data is Ratio scale of measurement.

An appropriate center measure cannot be mentioned if the data is Ordinal scale of measurement. But if the data is Ratio scale of measurement, mean amount of beer drunk by the first, second and third winner will be the appropriate center measure.