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# Custom Statistics Essay

In the field of statistics, the term measurement is used to represent the manner in which numbers categorized or grouped. These are called scales of measurement. Every scale of measurement contains characteristics that affect the relevance of these numbers for analysis in statistics. These scales are nominal, interval, ordinal and ratio scales. It is important that the differences between these four methods are taken to consideration in order to know exactly how best to apply them. The scale assigned to a variable always depends on its numerical characteristics (Valente and Sarli 2011). The type of scale chosen influences the mathematical operations which can be done on the variables. Consequently, this also affects the choice in statistical operations. The nominal scale has the lowest mathematical operations followed by ordinal scale. The interval scale has a higher number of mathematical operations then ordinal and nominal (Stephens 2009). The ratio scale has the most number of mathematical operations.

The Discussion

The nominal scale of data is the lowest level of measurement in statistics. It involves assigning a scale to items divided into different categories without paying any attention to a particular order. The number is assigned to the item for the purpose of identification, and even though the scale appears to descend or ascend there still remains no order. For example, fruits can be categorized into oranges, apples and pears (Valente and Sarli 2011). Numbers can be assigned to represent each category (oranges-1, apples-2 and pears-3). That represents a nominal scale. The only mathematical action that can be done on the data is a count. In the field of research the example of a nominal scale is a yes/no scale.

The ordinal scale of data presentation is an order of responses. A good example is that of athletes crossing the finish line in a race (Stephens 2009). The ranking 1, 2 and 3 represents an ordinal scale. The scale does not have an equal distance between the responses (i.e. Distance between 1 and 2, is not the same as that of 2 to 3). However, these responses have an order that they follow unlike the nominal scale. The scale analyses the order in which items follow without regard to the distance in between. The scale has the characteristic of magnitude and identity. The scale represents a quality being measured and can indicate to us whether a situation requires more of the identity or the magnitude (Valente and Sarli 2011). The scale is used in the process of ranking which is commonly used in day to day life.

The interval scale is commonly found in the usual survey type of rating. When a customer is asked about how well the product satisfies him or her based on a scale of one to five (excellent-1, very good-2, good-3, satisfactory-4 and o.k.-5) the interval scale is in use. The term interval is used because there is an equal interval between each value along the scale (Stephens 2009). In the interval scale the distance between the intervals is what bears significance based on how they are interpreted. The interval scale has the qualities of equal distance, magnitude and identity. These qualities assist one in identifying the interval scale.

The ratio scale is considered the best for of scaling variables because a variety of mathematical operations can be performed on it. The ratio scale is clearly defined by the presence of a zero point. The measurement of the length of a material or the measurement of money best exemplifies the scale. Having zero money simply means that there is no money at all. The ratio scale is also demonstrated in the measurement of temperature (Stephens 2009). The characteristics of the scale include the absolute zero, equal distance, magnitude and identity. The scale can accommodate all possible mathematical operations in statistics (Valente and Sarli, 2011). Any variables that contain the aforementioned characteristics fall into the ratio scale.

The Spread Sheets

The data points that are presented have got intervals, equal distance, order and the skewness indicates that the data has got a zero point. The data can be classified in the category of ratio scale due to the presence of the aforementioned characteristics.

The data points also fit into ratio, interval, and ordinal scales. This is due to the fact that the data points fulfill all the characteristics in all the categories above. However, the best scale to use in the data points is the ratio scale since most mathematical operations are applicable in the field of statistical analysis for this scale.

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