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.
(a) To get the mean, compute the average of those numbers.
(b) The median is the number in that group that is less than 7 and greater than 7 of the other numbers.
(c) What do YOU think? The median is not affected by the how well the best student does or how poorly the worst student does, but the mean is. The median mainly tells how well the "average student", in the middle of the class, did.
To find the mean final examination score, you need to compute the sum of all the scores and then divide it by the number of scores.
(a) Mean final examination score:
To find the sum of scores, add up all the numbers:
193 + 185 + 163 + 186 + 192 + 135 + 158 + 174 + 188 + 172 + 168 + 183 + 195 + 165 + 183 = 2780.
Next, divide the sum by the number of scores, which is 15:
2780 / 15 = 185.333.
So, the mean final examination score is 185.333.
(b) To find the median final examination score, you need to arrange the numbers in ascending order first and find the middle value(s).
Arranging the scores in ascending order:
135, 158, 163, 165, 168, 172, 174, 183, 183, 185, 186, 188, 192, 193, 195.
Now, find the middle value(s). In this case, there are two middle values, since there is an even number of scores (15). The two middle values are 183 and 185.
Therefore, the median final examination score is the average of these two values:
(183 + 185) / 2 = 184.
(c) Which is a more useful representative, the mean or the median?
To determine this, we need to consider the distribution of the scores. If the distribution is skewed or contains outliers, the median is generally a more useful representative since it is not influenced by extreme values. On the other hand, if the distribution is symmetrical and without outliers, the mean is a more appropriate representation as it considers all the scores equally.
In this case, without further information about the distribution or potential outliers, it is difficult to definitively say which measure is more useful. However, both measures provide valuable information about the final examination scores.