Descriptive statistics

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nTopic 50

nThe mean is the most frequently used average score. Mean is the balance point in a distribution. This is because the positive and negative deviations balance each other causing the deviation to balance at zero. It is calculated in the distribution by the sum of the scores divided by the number of scores (Patten, 2007). In addition, in academic journals mean is usually denoted as M, for the mean of a population, while m, is the mean of the sample. Nonetheless, in statistics the mean is usually denoted as x̅. Its pronunciation is X-bar. The formal definition of mean; it is the value around which the deviations sum to zero. This shows that in order to obtain deviation, the mean of the distribution is subtracted from the scores in the distribution (Patten, 2007). However, the sum of the deviations equals to zero.

nThe median is referred to as middle score. The researcher frequently use median when a distribution is highly skewed. To obtain the median the score are arranged in order from the lowest to the highest and then the middle score is determined. For instance, if there are nine scores in a group data, the researcher arranges the scores from the lowest value to the highest (Patten, 2007). Eventually, he determines the value at the center (middle score). This value is at the fifth position. Median is useful in statistics because it describes the average of ordinal data.

nTopic 51

nThe mean is the average that is reported together with standard deviation. Variability refers to the amount by which the participants differ or vary from each other. For instance, Group A has the following scores 0, 5, 10, 15, 20, 25, 30, with a mean of 15 and standard deviation of 10. Group B has 14, 14, 14, 15, 16, 16, 16 and mean of 15 but the standard deviation of 0.93 (Patten, 2007). This shows that although the two groups have the same mean, they have different variability. The group A scores have a high variability as compared to group B scores. However, if a group has the same scores, for instance, 15, 15, 15, 15, the standard deviation is zero hence there is no variability (Patten, 2007). In a normal distribution curve, 68 percent of the participants in the distribution lie within one standard-deviation unit of the mean

nTopic 52

nIf the median for a group of participants is 25.00, 50 % of participants have scores above a score of 25.00. This is because the median is the middle score in a distribution. In an ordinal data, the mean and the median should not be used together. Therefore, median should be used instead of mean in ordinal data (Patten, 2007). This is because ordinal data distribution is highly skewed. The range of a set of scores is calculated by subtracting the lowest score from the highest score. For instance, if the highest score is 20 and the lowest score is 5 the range is 15. Since the median involves two extreme scores, it is unrealistic as compared to interquartile range. Interquartile range is the range between quarters (Patten, 2007). Therefore, it is the range of the middle two quarters. The researcher, first divide the scores into quarters and then determines the median between them. Finally, he subtracts the highest median from the lowest median.

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nPatten M. (2007), Understanding the Research Methods. An overview of essentials (6th ed.) Glendale