If a set of data has 5 numbers has a range of six median of ten and a mean of ten what are the five numbers?

7,9,10,11,13 Assume the data list from smallest to largest is A,B,C,D,E. Then from the info given C=10 since 10 is the median. Also the range of the data is 6, so that means that E-A = 6. Since the mean of the data is 10 then (A+B+C+D+E)/5 = 10 or A+B+C+D+E = 50 You can substitute the value for C and E = 6+A (since the range is 6) to get A+B+10+D+(6+A) = 50 or simplified: 2A + B + D =34 Now since the median of the data is 10 the value of B will be less than 10 and A will be less than B. The value of D will be greater than 10 and E will be greater than D. To figure out the data list use trial and error. Start by picking a value of D > 10. Start with 11. From the equation above you have 2A + B + 11 = 34, now pick a value of B < 10. Start with 9 and substitute to solve for A. 2A + 9 + 11 = 34 or 2A = 14 and A=7 So A=7, B=9, C=10, D=11 and E=6+A or 13. To check see if these numbers equal the mean of 50. (7+9+10+11+13)/5 and it does. If it didn't work then you'd have to go back and pick values of B, D again until it does. Hope that helps.