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.
a- 176 is the mean
not sure on the rest, sorry
Mean= The "mean" is the "average" you're used to, where you add up all the numbers and then divide by the number of numbers.
Median= The "median" is the "middle" value in the list of numbers. To find the median, your numbers have to be listed in numerical order, so you may have to rewrite your list first.
For example:
take the set 1,2,5,4,2,3,7,4,1
Mean/average=
(1+2+5+4+2+3+5+4+1)
------------------- = 3
9
Median= 1,1,2,2,3,4,4,5,5 so the middle number would be 3.
Now which do you think better represents the set of data?
To find the mean final examination score, you need to calculate the average of all the scores. Here's how to do it:
Step 1: Add up all the scores: 193 + 185 + 163 + 186 + 192 + 135 + 158 + 174 + 188 + 172 + 168 + 183 + 195 + 165 + 183 = 2619.
Step 2: Divide the sum by the total number of scores. In this case, there are 15 scores: 2619 / 15 = 174.6.
So, the mean final examination score is 174.6.
To find the median final examination score, you need to determine the middle value when the scores are arranged in ascending order. Here's how to do it:
Step 1: Arrange the scores from lowest to highest: 135, 158, 163, 165, 168, 172, 183, 183, 185, 186, 188, 192, 193, 195.
Step 2: Find the middle score. In this case, there are 15 scores, so the middle position is the 8th value. The 8th value is 183.
So, the median final examination score is 183.
Now, let's compare the mean and median to determine which one is a more useful representative of the final examination scores.
In this case, the mean is 174.6 and the median is 183. Comparing the two, we can see that the median is slightly higher than the mean.
In general, if the distribution of scores is symmetric and close to a normal distribution, then the mean would be more useful as it takes into account all the values. However, if the distribution is skewed or has outliers, the median is a better measure because it is less affected by extreme values.
Therefore, in this case, since the distribution of scores is not given, it is difficult to make a definitive judgment. However, if there are any outliers or extreme values that might skew the data, the median would be a more useful representative of the final examination scores.