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As there are two numbers, the range is the difference between them
As there are 2 numbers the mean is exactly in the middle of them.
Thus half the range is less than the mean and half the range is greater than the mean.
Thus the two numbers are 10 ± (4/2) = 10 ± 2 = 8 and 12.
Algebraically, this can be seen:
Let the two numbers be x and y with y > x
Then:
- their range is y - x = 4; and
- their mean is (x + y) / 2 = 10
- {2} can be rearrange to give x + y = 10 × 2 → y + x = 20
- adding {3} to {1} yields: (y + y) + (-x + x) = 20 + 4 → 2y = 24 → y = 12
- subtracting {1} from {3} yields (y - y) + (x - -x) = 20 - 4 → 2x = 16 → x = 8
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What 2 numbers have a mean of 10 and a range of 4?
eight and twelveas mean is 10 then startwith 10 then divide the range of 4 by 2 = 2and take 2 off and add 2 on10 - 2 = 8 and 10 + 2 = 12Check:8 + 12 = 20 then divide those 2 numbers by that 2 so 20 / 2 = 10 mean12 - 8 = 4 range
Which 2 numbers have a mean of 10 and a range of 8?
To find two numbers with a mean of 10 and a range of 8, we can set up a system of equations. Let x be the smaller number and y be the larger number. We know that (x+y)/2 = 10 (mean of 10) and y-x = 8 (range of 8). Solving these equations simultaneously, we get x = 6 and y = 14. Therefore, the two numbers are 6 and 14.
Which two numbers have the mean of 10 and the range of 8?
6 and 14 Solution x - y= 8, so x =8 + y, (x + y)/2 = 10, x + y = 20, Substituting x = 8 + y, we have: 2 y + 8 = 20, or 2y = 12, y = 6, x = 6+8= 14
What numbers have the mean of 10 and the range of 12?
four and sixteen16 - 4 = 1216 + 4 = 20 then 20 / 2 = 10Half of 12 is 6, therefore the two numbers 10 - 6 = 4 and 10 + 6 = 16 will have a mean of 10 and a range of 12.Further numbers can be added between 4 and 16 as long as their mean is still 10, eg the data sets:{4, 16}{4, 10, 16}{4, 8, 12, 16}{4, 8, 10, 12, 16}{4, 7, 9, 14, 16}all have a mean of 10 and a range of 12. There is an infinity of such sets.
How do you find the range of a group of numbers?
To find the range of a group of numbers, subtract the smallest from the largest. examples: * range of {6, 8, 12, 19, 27} is 27 - 6 = 21 * range of {5, -2, 1, 10, 18} is 18 - (-2) = 18 + 2 = 20
