Data Set With Specified Mean, Median, Range
Date: 12/11/2003 at 18:52:58 From: Anita Subject: How do I find the mean, median and range? The problem is: Make up a set of 5 numbers with a mean of 20, a median of 10, and a range of 50. So this is what I came up with for a mean: 1 + 3 + 4 + 5 + 7 = 20 Now my median is supposed to be 10 but if you look at my selections my median is 4. I cannot get a mean of 20 with 5 numbers and then get a median of 10. I don't get it.
Date: 12/11/2003 at 23:52:08 From: Doctor Jason Subject: Re: How do I find the mean, median and range of a number Hi Anita, Thanks for writing to Dr. Math! I would like to address the 4 parts of your problem in the following order: 1. A set of 5 numbers 2. the median is 10 3. the range is 50 4. the mean is 20 The first part of the problem is pretty straightforward. We can create 5 blanks to provide a place to record our 5 numbers. _____ ______ ______ ______ ______ For the second part of the problem, we need a median of 10. What this means is that the middle value of the set, when the numbers are in order from least to greatest, must be 10. We can enter the number 10 in the middle position. _____ ______ __10__ ______ ______ Having a range of 50 means that when we subtract the smallest number from the largest number, the difference must be 50. For example, we can make the smallest value 5, which means the largest value must then be 55. __5__ ______ __10__ ______ __55__ To satisfy the last requirement, we need have a mean of 20. The mean of a set of numbers is the sum of the values divided by the number of values. Since we know that we have 5 numbers and the mean must be 20, we can calculate what the sum of our 5 digits must be: sum of digits mean = ---------------- number of digits ? 20 = ---------------- 5 digits Based on the equation above, the sum of our 5 digits must be 100. So far we have a sum of 70 (5 + 10 + 55 = 70). The difference between 100 and 70 is what we have left to share between the two remaining blanks. Remember that one of the blanks needs a value between 5 and 10, while the other needs a value between 10 and 55. I believe that there are four different pairs of numbers that may be used to finish the problem as we have started it. There are many other possible solutions if you start with numbers other than 5 and 55. Can you take it from here? - Doctor Jason, The Math Forum http://mathforum.org/dr.math/
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