A test given to a class of students revealed that most did quite well, and only a few did very poorly. How would you describe the distribution of test scores? Would you want to report the mean, median, or mode for this distribution? Please explain the answer.
It seems like your distribution is negatively skewed (skewed left, with the tail pointing to the left on a frequency distribution).
The mean (as a balance point for the distribution) is most influenced by deviant scores, and the mode just indicates what value had the most scores. Thus the median would be the most central of the measures of central tendency.
Does that help?
Can you explain this in alittle more detail? I am having a hard time understanding.
What don't you understand?
Make up a frequency distribution that fits the above description.
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Insert numerical values and find the measures of central tendency for that distribution to see where they are. Does this help a little more?
To describe the distribution of test scores, we need to understand the relative frequencies of different score ranges.
If most students did quite well and only a few did very poorly, the distribution is likely skewed to the right. This means that the majority of scores are concentrated towards the higher end, with fewer scores at the lower end.
To determine whether to report the mean, median, or mode for this distribution, we need to consider the characteristics of each measure and how they are affected by skewed distributions:
1. Mean: The mean is the average of all the scores. It can be influenced by extreme values, especially in skewed distributions. In the case of a skewed right distribution, the few very low scores would pull the mean towards the lower end, making it lower than the typical score.
2. Median: The median is the middle value when all the scores are arranged in ascending order. It is not affected by extreme values or the shape of the distribution. Since most students did quite well, the median would likely be a good measure to report because it represents the typical score.
3. Mode: The mode is the most frequently occurring score. In a normal distribution, the mode, median, and mean are all equal. However, in skewed distributions, the mode may not accurately represent the center of the distribution. In this case, the mode may be a score that only a few students achieved, but it is not reflective of the majority of the scores.
Given the information provided, it would be ideal to report the median for this distribution because it represents the typical score and is not influenced by extreme values or the shape of the distribution.