Normalize a list containing only positive data into a range comprising negative and positive values

I have a list of data that only contains positive values, such as the list below:

data_list = [3.34, 2.16, 8.64, 4.41, 5.0]

Is there a way to normalize this list into a range that spans from -1 to +1?

The value 2.16 should correspond to -1 in the normalized range, and the value 8.64 should correspond to +1.

I found several topics treating the question of how one can normalize a list that contains negative and positive values. But how can one normalize a list of only positive or only negative values into a new normalized list that spans from the negative into the positive range?

With [tag:numpy], you can use interp:

#pip install numpy
import numpy as np
data_list = [0.54, 2.16, 8.35, 0.35, 1.1]
out = np.interp(x=data_list, xp=(min(data_list), max(data_list)), fp=(-1, +1)).tolist()

Output :

print(out)
# [-0.9525, -0.5475, 1.0, -1.0, -0.8125]

You don't need to import libraries for a task like this. The normalisation maths is quite simple.

To normalise between 0 and 1, take each value, subtract the minimum value of the list, then divide by the maximum value minus the minimum value.

def normalise(data):
	data_max=max(data)
	data_min=min(data
	for i,n in enumerate(data):
		data[i]=(n-data_min)/(data_max-data_min)
	return(data)

To then change the range that it is scaled to, you need to multiply it by the span of the range (i.e., abs(max_value-min_value)) then add the lower limit.

def normalise_to_range(data,min_value,max_value):
	data_max=max(data)
	data_min=min(data)
	span=abs(max_value-min_value)
	for i,n in enumerate(data):
		data[i]=span*(n-data_min)/(data_max-data_min)+min_value
	return(data)

Using your data and setting the range to -1,1:

data_list = [0.54, 2.16, 8.35, 0.35, 1.1]
normalise_to_range(data_list,-1,1)
#[-0.9525, -0.5475, 1.0, -1.0, -0.8125]

While there are ready-made lib functions available, you can very easily replicate that logic with a simple list comprehension.

data_list = [3.34, 2.16, 8.64, 4.41, 5.0]
minL = min(data_list)
maxL = max(data_list)
normalised = [((x - minL) * 2)/(maxL - minL) - 1 for x in data_list]
print(normalised) # [-0.6358024691358026, -1.0, 1.0, -0.3055555555555556, -0.1234567901234569]