Which measure of central tendency is based on all the scores in the distribution?
Show Three primary pieces of information are typically used to provide indicators of subjects' performances in data. These three pieces of information are: the shape of the distribution of scores (symmetrical, positively or negatively skewed), its "average" or typical score (e.g., mean, median, or mode), and the spread or variability of the scores in the
distribution (e.g., range, variance, and standard deviation). The shape of the distribution of scores is reflected in the relationship among the "average" or typical scores in that distribution. Although each measure of central tendency attempts to identify the most typical score in that distribution of scores, each measure has its own interpretation of the most typical score. The mean defines
central tendency as the mathematical average of all the scores (a measure that you are very familiar with). The median defines central tendency as the point where half the scores fall above that value and half the scores fall below it. Finally, the mode defines central tendency as the most frequently occurring score in that distribution of scores. If the data being analyzed is qualitative, then the only measure of central tendency that can be reported is the mode. However, if the data is quantitative in nature (ordinal or interval/ratio) then the mode, median, or mean can be used to describe the data. With quantitative data, the shape of the
distribution of scores (symmetrical, negatively or positively skewed) plays an important role in determining the appropriateness of the specific measure of central tendency to accurately describe the data. If the distribution of scores is symmetrical or nearly so, the median and mean (as well as the mode) will be real close to each other in value. In this case, the mean is the value of central tendency that is usually reported. However, if the distribution of scores is
positively or negatively skewed, the mean will tend to either overestimate (in positively skewed distributions) or underestimate (in negatively skewed distributions) the true central tendency of the distribution. In extreme cases of skewed data, the mean can lie at a considerable distance from most of the scores. Therefore, in skewed distributions, the median will tend to be the more accurate measure to represent the data than the mean because the median can never have more
than one half the scores above or below it. As with measures of central tendency, different measures of dispersion are appropriate for different problems. The most common measures of dispersion are the range, variance, and standard deviation. The appropriateness of each would depend, in part, on the type of data that you have and which measure of central tendency you are using. If the data is qualitative, then there is no measure of variability to report. For data that is quantitative (ordinal and interval/ratio) all three measures are possible. However, the shape of the distribution of scores and the measure of central tendency reported will determine which measure of variability to use. If the distribution of scores is symmetrical in nature, then the measures of variability usually reported are the variance and standard deviation, although the standard deviation would be more interpretable. However, if the data is skewed, then the measure of variability that would be appropriate for that data would be the range. In summary, with qualitative data, the only additional measure to be
concerned with to further describe that data would be the mode. With quantitative data, the mean, variance, and standard deviation would be appropriate with symmetrical distributions while the median and range would be appropriate when the distribution is skewed (either positively or negatively). Which measure of central tendency is best to use when all scores are nominal?The mode is the least used of the measures of central tendency and can only be used when dealing with nominal data. For this reason, the mode will be the best measure of central tendency (as it is the only one appropriate to use) when dealing with nominal data.
Which of the measure of central tendency based on all the observations?The mean is the sum of the value of each observation in a dataset divided by the number of observations. This is also known as the arithmetic average.
What are the central tendency measures of distribution?The central tendency measure is defined as the number used to represent the center or middle of a set of data values. The three commonly used measures of central tendency are the mean, median, and mode.
What measure of central tendency best describes the center of the distribution?Since the data set is not skewed, the central tendency that best describes the "center" of the distribution is the mean. The arithmetic mean of a variable is computed by adding all the values of the variable in the data set and dividing by the number of observations.
|