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The median of a set of data is used for similar purposes as the mean. They both give you a middle number that represents what the set of data fluctuates around. While the mean gives you the exact center, the median simply gives you the middle piece of data. The following is an example of why the median is sometimes more helpful than the mean:
Consider a class of 5 students that take a test that is scored on a scale of 0 to 500. The scores of the students are as follows:
1) 25
2) 120
3) 102
4) 248
5) 500
The mean of the scores is (25+120+102+248+500)/5 = 199
The median of the scores is 120
Looking only at the mean, the teacher may get the impression that the students are more skilled than they really are, since the average score of the class is 40% of the highest possible score. However, one student scored only 49 points higher than the mean and the other 3 didn't get within 70 points of it.
Looking at the median, the teacher sees that another accurate representation of the scores is 120. This is only 24% of the highest possible grade and better represents what most of the class got. Unlike the mean, the median wasn't set deceivingly high by the one student with a perfect score.
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When is it misleading to use the mean as a descriptor of a data set?
It is misleading to use the mean as a descriptor of a data set when the median or mode would be more representative of the data set as a whole.
What measure of center best represents data?
The answer depends on the type of data. The mean or median are useless if the data are qualitative (categoric): only the mode is any use. The median is better than the mean is the data are very skewed.
When do you use mean median and mode?
You use mean when you want to find the average of data. You use median to find the middle of a piece of data, ordered from least to greatest. If there is 2 medians, then find the average of those 2 numbers. You use mode when you are trying to figure out the most common piece of data. There can be more than 1 mode.
How do you find median of the data 24 25 26 27 28 29 30 31 32 33?
Well, honey, to find the median of that data set, you line those numbers up in order, from smallest to biggest. Since there are 10 numbers, the median will be the average of the 5th and 6th numbers. In this case, it's 28 + 29 divided by 2, which equals 28.5. Voilà!
What is the formula for getting the median of the ungrouped data?
You will need to put the un-grouped data in ascending or descending order. If you have an odd number of data values the formula for the median value is (n+1)/2. Example my data in ascending order is 0, 2, 4, 5, 7, 8, 9. I have 7 data values. The median is the value (7+1)/2 = 4th value from left or right which is 5. For an even number of data values, you will need to calculate the median and it may not be a data value. It will be the mean of the two center values. Use the formula n/2 to get the left most value. Example my data in ascending order is 0, 2, 4, 5, 7, 8. I have 6 data values. The left most value I will use to calculate the median is 6/2 = 3rd. The 3rd value from the left is 4. The next value is 5. Median is (4+5)/2 = 4.5.
