# Data transformation: new min, max and mean

I have a dataset of 31 values, of which the $$min = -0,8,\ max = 11, 1$$ and $$mean = 5,0$$.

Is there a way to transform these data to a $$\text{new} \ minimum (0.3), \ \text{new} \ maximum (11.4)$$ and $$\text{new} \ mean (5.3)$$?

Thanks!

6,7
4,9
4,5
3,0
4,6
1,9
2,7
4,0
2,3
6,4
7,6
6,2
6,7
6,3
11,1
9,1
8,3
8,3
4,5
5,6
5,6
5,9
4,4
5,9
2,4
0,7
1,0
-0,8


One way would be to use a quadratic equation to change every value in your dataset from $$x_i$$ to $$y_i= a \cdot x_i^2+b \cdot x_i+ c$$. The equation for the new minimum would then be $$0.3 = a \cdot (-0.8)^2+b \cdot (-0.8) + c\tag{1}$$ The equation for the new maximum would be $$11.4 = a \cdot (11.1)^2+b \cdot (11.1) + c \tag{2}$$ And the equation for the new mean would be $$5.3 = \frac{1}{31}\sum_{i=1}^{31} (a \cdot x_i^2+b \cdot x_i + c)$$ or $$5.3 = a \cdot \frac{1}{31}\sum_{i=1}^{31} x_i^2+b \cdot (5.0) + c \tag{3}$$ Assuming equations $$1$$, $$2$$ and $$3$$ are linearly independent you could work out the values of $$a$$, $$b$$ and $$c$$.