Business and finance. The following scores were recorded on a 200-point final examination:193, 185, 163, 186, 192, 135, 158, 174, 188, 172, 168, 183, 195, 165, 183.(a) Find the mean final examination score.(b) Find the median final examination score.(c) Is the mean or median a more useful representative of the final examination scores? Write a brief paragraph justifying your response.
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To find the mean final examination score, we sum up all the scores and divide by the number of scores. Here's how you can calculate it:
(a) Mean:
1. Add up all the scores: 193 + 185 + 163 + 186 + 192 + 135 + 158 + 174 + 188 + 172 + 168 + 183 + 195 + 165 + 183 = 2727.
2. Divide the sum by the number of scores, which is 15: 2727 / 15 = 181.8.
Therefore, the mean final examination score is 181.8.
To find the median final examination score, we need to arrange the scores in numerical order and find the middle value. Here's how to do it:
(b) Median:
1. Arrange the scores in numerical order: 135, 158, 163, 165, 168, 172, 183, 183, 185, 186, 188, 192, 193, 195.
2. Since we have an odd number of scores (15), the median will be the middle score. In this case, it is the 8th score: 183.
Therefore, the median final examination score is 183.
(c) To determine whether the mean or median is a more useful representative of the final examination scores, we need to consider the distribution of the scores. If the scores are evenly distributed, the mean will be a better representation. On the other hand, if the scores are skewed or have outliers, the median will be more reliable.
In this case, without further information about the distribution of the scores, it is difficult to definitively say which measure is more useful. However, it is worth noting that the mean is more sensitive to extreme values since it takes into account every score, whereas the median is not influenced by extreme values. Therefore, if there are any outliers or extreme scores, the median might provide a more accurate representation of the majority of the scores.