Research Misconceptions: Mean, Mode and Median (Essay Sample)
When people read, hear, or prepare research summaries, they sometimes have misconceptions about what is or isn't "sound practice" regarding the collection, analysis, and interpretation of data. Here are some of these common (and dangerous) misconceptions associated with descriptive statistics.
Choose three of these, and explain why they are misconceptions.
1. The mean is superior to either the median or the mode.
2. If a mean and a standard deviation are cited for a group of data, those two indices "say it all."
3. Data that approximate the normal distribution are superior to data that are skewed.
4. Frequency distributions, bargraphs, stem-and-leaf displays, and box plots are so elementary that they don't belong in sophisticated research summaries.
5. A standard deviation indicates how far a typical score will deviate from the mean.
6. The highest score in a group will always be about six standard deviations higher than the lowest score in that group.
7. If drawn correctly, a normal curve must resemble a bell.
8. Standard scores (such as z-scores or T-scores) are computed by researchers only when the original data are normally distributed.
9. The only three measures of central tendency are the mean, the median, and the mode.
10. The word "average" is synonymous with the word "mean."
11. The normal curve is curved most at the points of inflection (i.e., above the baseline points of z = +1.0 and z = -1.0)
12. If the male test scores have a SD = 10 and the female test scores have a SD = 20, the SD for the combined group of males and females will be equal to 15.
When conducting a research project, the researchers describe the fundamental features of the data in the study through descriptive statistics. Every quantitative data measured and collected from samples during research is summarized, and graphical representations are created for analysis. This procedure is common in all quantitative data analysis. Descriptive analysis is used to elaborate what the data collected from the study reveals. In some cases, research might involve a large group of people. Thus, the incorporation of descriptive statistics enables researchers to simplify the data collected in a manageable manner.
There are several misconceptions about descriptive statistics that often mislead researchers when analyzing their data. Such misconceptions hinder the researchers from making correct sense of their statistical information such as spread, center, and distribution (Bennett & Anway, 2003). This essay seeks to explain three misconceptions that associated with the descriptive analysis. The misconceptions are the mean is superior than the median and mode, the word ‘average’ is synonymous to the word ‘mean,’ and the only valid central tendency measures are mean, mode and median.
The Mean is Superior than Mode and Median
The most commonly used measures of central tendency are mean, mode and median. Although the mean is common among the three, it is not greater than median and mode. Whenever the values from observations are arranged in order, either descending or ascending, the median always occupies the middle position. This means that it equally divides the frequency distribution into two (Manikandan, 2011). Since the median is the middle number, it is more advantaged than the mean since it is not affected by outliers. In cases where the data collected has extreme values, the median is a better choice when calculating central tendency compared to mean. The mode is the most recurring value in the data. Some data do not have numbers that reoccur, and this makes it difficult to rely on the mode. However, in bi-modal distribution, mode is commonly used as the summary statistic. Nonetheless, in most cases, mean is regarded as the most appropriate measure of central tendency....
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