Normalise between 0 and 1 ignoring NaN

Here's a different approach and one that I believe answers the OP correctly, the only difference is this works for a dataframe instead of a list, you can easily put your list in a dataframe as done below. The other options didn't work for me because I needed to store the MinMaxScaler in order to reverse transform after a prediction was made. So instead of passing the entire column to the MinMaxScaler you can filter out NaNs for both the target and the input.

Solution Example

import pandas as pd
import numpy as np
from sklearn.preprocessing import MinMaxScaler

scaler = MinMaxScaler(feature_range=(0, 1))

d = pd.DataFrame({'A': [0, 1, 2, 3, np.nan, 3, 2]})

null_index = d['A'].isnull()

d.loc[~null_index, ['A']] = scaler.fit_transform(d.loc[~null_index, ['A']])

consider pd.Series s

s = pd.Series(np.random.choice([3, 4, 5, 6, np.nan], 100))
s.hist()

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Option 1
Min Max Scaling

new = s.sub(s.min()).div((s.max() - s.min()))
new.hist()

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NOT WHAT OP ASKED FOR
I put these in because I wanted to

Option 2
sigmoid

sigmoid = lambda x: 1 / (1 + np.exp(-x))

new = sigmoid(s.sub(s.mean()))
new.hist()

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Option 3
tanh (hyperbolic tangent)

new = np.tanh(s.sub(s.mean())).add(1).div(2)
new.hist()