the following scores were recorded on a 200-point final wxam 193,185,186,192,135,158,174,188,172,168,183,195,165,183. what is the mean please and is the mean or the median mor improtant for this
Please see the other posts to figure out how to find the mean.
Since these are grades on an exam, most teachers use the mean (average) to determine the curve. The median is not important for this.
ƒÊ = (ƒ°X)/N, where ƒÊ is the mean, ƒ° is a math symbol telling you to add whatever follows, X = raw scores and N = number of scores.
For a normally distributed distribution, the mean is the best measure of central tendency. The mean acts as a "balance point" for the distribution.
However, when the distribution is skewed (pulled out at either one end or the other), then the mean is unduly displaced by extremely deviant scores. In this case, the median (50th percentile) would be the best measure to use.
This can be easily seen with a simple distribution of scores: 1, 2, 3, 4 and 30. The mean would be 8, while the median would be 3. Since both are meeasures of central tendency, which do you think would be the best indicator?
To see if the distribution is skewed, you can plot the scores out by using a frequency distribution or a bar diagram.
I hope this helps a little more. Thanks for asking.
To find the mean, you need to sum all the scores and divide by the number of scores.
Sum of scores = 193 + 185 + 186 + 192 + 135 + 158 + 174 + 188 + 172 + 168 + 183 + 195 + 165 + 183 = 2519
Number of scores = 14
Mean = Sum of scores / Number of scores = 2519 / 14 = 179.93 (rounded to two decimal places)
So, the mean is approximately 179.93.
As for whether the mean or the median is more important for this dataset, it depends on the specific context. However, since these are grades on a final exam, most teachers use the mean to determine the average performance of the students. The mean gives equal weight to all the scores, which is important when calculating a class average. So, in this case, the mean would be more important.
To find the mean of the given scores, you need to add up all the scores and divide by the total number of scores.
So, let's calculate the mean for the given scores:
193 + 185 + 186 + 192 + 135 + 158 + 174 + 188 + 172 + 168 + 183 + 195 + 165 + 183 = 2519
There are 14 scores in total, so the mean is 2519 divided by 14:
2519 / 14 ≈ 179.93
Therefore, the mean of the scores is approximately 179.93.
As for whether the mean or median is more important, it depends on the context and purpose of the analysis. In this case, since the scores are on a 200-point final exam, the mean is typically used to determine the average performance. However, if there are extreme outliers or the distribution is heavily skewed, the median may be a better measure of central tendency. Ultimately, it depends on the specific requirements and objectives of the analysis.