Que 4(b): Are the following Nominal, Ordinal, Interval or Ratio data? Explain your answer?
Measurement is the process of assigning numbers to objects or observations. In other words, it is some form quantification expressed in numbers. Data/ scales of measurement in terms of their mathematical properties can be grouped as nominal, ordinal, interval and ratio. Nominal (name and count) •
Order is of no sequence
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Data are numerical in name only
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Scale assigns number symbols to events in order to label them
Ordinal (rank or order) •
Scale places events in order
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Intervals of the scale are not equal
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Rank order correlations are possible
Interval (score/ mark) •
Mean is the appropriate measure of central tendency
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Equality of interval
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More powerful than ordinal scale
Ratio •
Most precise scale
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Scale has absolute zero which represents amount of variables
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Co-efficient of variation can be calculated
1. Temperature measured on Kelvin scale
Temperature measured on Kelvin scale is an example of interval scale.
Reason:
It has an identity as well as a magnitude.eg. 278K means a definite temperature. The intervals are adjusted in terms of some rule that has been established as a basis for making the units equal. There is an arbitrary zero. There is a concept of absolute zero in Kelvin scale, where all the molecular movement
November 18, 2009
ASSIGNMENT_RM
Group-10
ceases but it is only theoretical. Mean is the appropriate measure of central tendency, we always talk of average temperature. We cannot say that 546 K is twice the temperature of 273 K.
2. Military ranks
Military ranks are an example of ordinal scale.
Reason:
Military ranks are ORDINAL TYPE OF DATA because it has both Identity and Ranking (Magnitude) i.e. there is a value to each rank. It is not nominal data, because in nominal data there is no ranking, where as in the military the ranks are important are cannot be interchanged, they have a definite hierarchical structure. It is not Interval type of data because there are no equal intervals between the ranks in the military. It is not Ratio type of data because there is no equal interval between ranks and neither is there an absolute zero (i.e. there is no position in the military which does not have a rank associated with it)
3. Social Security Numbers
Social security numbers can be classified and put under the Nominal Scale. Reason:-
Nominal Scale is a system of assigning number symbols to events in order to label them. Social Security Numbers are just assigned to the citizens of a country. Their order is not of consequence and the numbers just act like convenient labels for the particular class of people. Nominal Scales provide convenient ways of keeping track of people which is exactly what social security numbers are assigned for. It cannot be classified under the ordinal scale because, an ordinal scale places events in order and ranks them and the scale is used in research. Similarly it cannot be classified under the Interval scale because an interval scale can be used when there is an arbitrary zero. Interval scale is used when there is a need to identify, to see the magnitude and there is an equal ratio between the two units. In the same way, a ratio scale cannot be used because the use of a ratio scale demands that there should be a true zero the ratio of units should be equal there should be magnitude and identity. A ratio Scale represents the actual amount of variables.
November 18, 2009
ASSIGNMENT_RM
Group-10
4. Number of passengers on buses from Delhi to Mumbai
It is an example of ratio scale
Reason: A ratio scale is a measurement scale in which a certain distance along the scale means the same thing no matter where on the scale you are, and where "0" on the scale represents the absence of the thing being measured. Thus a "4" on such a scale implies twice as much of the thing being measured as a "2." Ratio scale have absolute or true zero of measurement. With ratio scales involvement one can make statements like jyoti’s typing performance was twice as good as ritu’s. The ratio involved has the significance and facilitates a kind of comparison which is not possible in case of interval scale. Ratio scale represents the actual amount of variables. Generally all statistical techniques are usable with ratio scale and all manipulations that one can carry out with real numbers can also be carry out with ratio scale values. Thus the number of passengers in bus from Delhi to Mumbai falls under the example of ratio scale because it can be “zero” and it signifies the actual amount of variables.
5. Code numbers given to religion of persons attempting suicide It is an example of Nominal Scale.
Reason: Nominal Scale is a system of assigning number symbols to events in order to label them. By giving code numbers, the people are just classified in their religion and the codes are purely for identification. Their order is not of consequence and the numbers just act like convenient labels for the particular class of people. Nominal Scales provide convenient ways of keeping track of people which is exactly what the codes assigned to the people do. It cannot be classified under the ordinal scale because, an ordinal scale places events in order and ranks them and the scale is used in research. Similarly it cannot be classified under the Interval scale because an interval scale can be used when there is an arbitrary zero. Interval scale is used when there is a need to identify, to see the magnitude and there is an equal ratio between the two units. In the same way, a ratio scale cannot be used because the use of a ratio scale demands that there should be a true zero the ratio of units should be equal there should be magnitude and identity. A ratio Scale represents the actual amount of variables.
