Question 200329: Hello tutor I'm new to this site can you help me with this problem .
Select five random numbers between 70 and 100. Calculate the mean, median, mode, and midrange of these numbers. Based on your calculations, which measure of central tendency best represents these numbers?
so greatful. Melissa
Found 2 solutions by jim_thompson5910, solver91311:
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! Here are the 5 Values:
72, 70, 99, 71, 74
Mean - Add up the values and divide the sum by 5:
So the mean is 77.2
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Median: First sort the values
70, 71, 72, 74, 99
We can see that the middle value is 72. So the median is 72.
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Mode: There isn't a mode since there are no repeated values.
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Midrange: Add up the smallest value and the largest value. Divide that sum by 2:
So the mid-range is 84.5
Notice how most of the data is clustered in the low 70's. So this means that the average value is in the low 70's. Since the median is 72 (which the closest value in the low seventies), this means that the median is the best measure in this case. Why? The extreme value 99 affects both the mean and midrange, but it doesn't affect the median.
Answer by solver91311(24713)  (Show Source):
You can put this solution on YOUR website!
You can pick your own five numbers.
1. Add them and divide the sum by 5. That is your mean.
2. Put them in numerical order. The one in the middle is the median.
3. Count the number of times each selected value appears. The one that appears most often is the mode. If all five numbers are different, then there is no mode.
4. Find the smallest one and the largest one, add them together and divide by 2. That is your midrange.
The one that best represents the middle of your numbers will depend on what numbers you choose. For example, if you chose 4 numbers less than 80 and one that was nearly 100, the midrange would be a lousy choice because the midrange would be in the mid- to high-eighties. The mean would not be a good measure of the center either because you would have something near or exceeding the high end of your group of 4 low numbers. In this case, the median would tell you the most about the center of the numbers. On the other hand, if the numbers were spread fairly evenly, then there would be little difference between the three. You will just have to evaluate the results that you get. The likelihood that there would even be a mode for a sample of size 5 from a population of 30 is relatively slim - 70% probability that all five would be different. But even if there is a mode, for such a small sample it would be a highly unlikely coincidence if the mode had any relationship whatsoever to the center of your data. Oh, and if you are actually full of gratitude for this, you would be grateful rather than greatful -- yes, spelling counts, even in mathematics.
John
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