Discuss the three properties of data and some of the descriptive measures (chara

Question

Discuss the three properties of data and some of the descriptive measures (characteristics) associate with each. Include a discussion of why it is important to review more than one measure of location when drawing conclusions about your data. Also discuss the importance of reviewing the standard deviation when you are presenting the mean to be representative of the "average " value of your data. (What does the standard deviation tell us about the mean's usefulness in portraying the "representative" average value of our data?).

Explanation / Answer

The three properties of data are as follows:

1. Distribution: The first step of any quantitative reserach project is to examine the variables and to see how the scores are distributed, that is frequency of individual values or a range of values across the variable. The most useful way is to construct tables, or frequency distributions, that report the number of cases in each category, for all variables. Thesse tables can be used with variables at any level of measurement. For example, for the variable, Gender (fictitous data) for a particular location the frequency distribution table is as follows:

Gender Frequency

Male 53

Female 60

N=113

Distribution can be displayed using percentages or proportionsto enhance clarity.

2. Central tendency: The benefit of frequency distributions is that they summarize the overall shape of a distribution of scores in a way that is quickly comprehended. However, to know more detailed information measure of central tendency is required.The three commonly used measure of central tendency are mean, median and mode.

Mean: The arithmatic average of the scores, Xbar represent the mean of sample, and mu is the mean of population.

Median: The point in a distribution of scores above and below which exactly half of the cases fall.

Mode: The most common score in the distribution.

3. Measure of Dispersion: Measure of dispersion gives a complete description of distribution of scores, as it includes variety, diversity, and heterogeneity of a distribution of scores.

Range: Range is the difference between highest and lowest score.

Standard deviation: The statistic computed by summing the squared deiations of the scores around the mean dividing by N, and finally taking sqaure root of the result.

Varince: The sum of scores around the mean, divided by N.

Amesure of dispersion is used primarily in inferential statistics and also in correlation and regression techniques, s^2 represent variance of sample, sigma^2 represent variance of a population.

The standard deviation is the most important measure of dispersion because of its central role in many more advanced statistical applications. The standard deviation has a minimum value of 0 9indicating no variation in the distribution) and increases in value as the variability of the distribution increases. It is used more appropriately with variables measured at the interval-level (note: mean is used as a measure of central tendency when, the variable is measured at interval-ratio level) but is also frequently computed for ordinal level variables.

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