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
http://www.purplemath.com/modules/meanmode.htm
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To find the answers to these questions, we will follow these steps for each part:
(a) Calculate the mean final examination score:
Step 1: Add up all the scores: 193 + 185 + 163 + 186 + 192 + 135 + 158 + 174 + 188 + 172 + 168 + 183 + 195 + 165 + 183 = 2693.
Step 2: Divide the sum by the number of scores (15 in this case): 2693 / 15 = 179.53.
Therefore, the mean final examination score is approximately 179.53.
(b) Find the median final examination score:
Step 1: Arrange the scores in ascending order: 135, 158, 163, 165, 168, 172, 183, 183, 185, 186, 188, 192, 193, 195.
Step 2: Since there is an odd number of scores (15), the median is the middle value, which in this case is the 8th score.
Therefore, the median final examination score is 183.
(c) Comparing the mean and median as representatives of the final examination scores:
In this case, the mean is 179.53, while the median is 183. When considering the usefulness of the mean and the median as representatives of the scores, it depends on the specific context and the characteristics of the distribution. If the data were normally distributed without any significant outliers, the mean would generally be more useful and representative. However, if there are outliers in the data, like the score of 135 in this case, the median is less affected by outliers and can provide a better representation. Additionally, the median can be more appropriate when dealing with skewed data. Thus, the choice between mean and median as the more useful representative of the final examination scores depends on the specific characteristics and context of the data.