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.
To find the mean add up all the numbers and then divide by how many numbers there are.
Median: First place all your numbers in order from least to greatest. Since you have an odd amount of numbers you will take the two middle numbers add them together then divide by two
Kara, if you have an odd amount of numbers, there will be a "middle" number
adding up the two middle numbers and dividing by 2 is done when you have an even count of numbers.
To find the mean final examination score, you need to calculate the average of all the scores recorded. To do this, add up all the scores and then divide the sum by the number of scores.
(a) Mean final examination score:
Add up all the scores: 193 + 185 + 163 + 186 + 192 + 135 + 158 + 174 + 188 + 172 + 168 + 183 + 195 + 165 + 183 = 2716
Divide the sum by the number of scores (15 in this case): 2716 / 15 = 181.07
Therefore, the mean final examination score is approximately 181.07.
To find the median final examination score, you need to arrange the scores in ascending order and then find the middle number. If there is an even number of scores, you take the average of the two middle numbers.
(b) Median final examination score:
Arranging the scores in ascending order: 135, 158, 163, 165, 168, 172, 183, 183, 185, 186, 188, 192, 193, 195
There are a total of 15 scores, so the middle number is the 8th score.
Therefore, the median final examination score is 183.
(c) Whether the mean or median is a more useful representative of the final examination scores depends on the context and purpose of the analysis.
The mean is more affected by extreme scores, so if there are outliers in the data, it can be greatly influenced by those outliers. The median, on the other hand, is not affected by extreme scores as it only considers the middle value(s). In this case, the scores do not show any extreme outliers, and the mean and median are close in value (181.07 and 183, respectively). Therefore, in this particular scenario, both the mean and median can be considered useful representatives of the final examination scores.