Normalize sample data for clustering I have three types of summary score, $a, b$ and $c$ for 200 samples.
$S1, S2, S3,..., S200$
$a_{s1}, a_{s2}, ..., a_{s200}$
$b_{s1}, b_{s2}, ..., b_{s200}$
$c_{s1}, c_{s2}, ..., c_{s200}$
Each of these scores is essentially the number of times that some event occurs in the data of each sample. I wish to find groups of these samples by correlation-based clustering. However, the scales for each of these scores are very different:
Summary of $a$:
Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
2.0   36.0   55.0   52.5   69.0  139.0 

Summary of $b$:
Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
8.0   99.5   285.0   292.7   737.5  2624.0 

Summary of $c$:
Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
40.0    111.0   176.0   300.4   554.5   779.0 

Should I have to normalize the scores? If so, how?
NB. I want to make no assumptions about the dependence or independence between these types of events and hence between these summary scores.
UPDATE:
So, I've decided to try clustering with Euclidean. In order to get normalized and transformed data, I'm doing the following:
1. test whether scores fit a normal distribution with Shapiro test


*

*if not, then do a boxcox transformation using $\lambda$ from a boxcoxfit

*get z-score for each score

*cluster with euclidean distance measure
Does this seem reasonable?
 A: Clustering in general requires a similarity metric to compute a partitioning of your data. Do you know how to compute the similarity of $\vec{a}$ to $\vec{b}$? Whether you need normalization or not will mainly depend on this question. If you don't have such a metric/measure, and you want to go with the regular Euclidean distance, normalizing your data -- bringing each variable to zero mean and unit variance -- would be recommended. Because if you don't, the scores with the largest range will dominate the distance computation. 
A: To perform z-score normalisation on x, you don't have to test whether x is of normal distribution or not.
For whatever distribution, z will be in a distribution of zero mean, one standard deviation.
Type of distribution matters when you use any test on the data, based on that particular distribution.
Convenience of normal distribution in this sense is that
if x is in normal distribution with mean m and standard deviation s
z (= (x-m)/s) will also be in normal distribution with mean zero and standard deviation 1.
====
Some people use the normalisation for clustering 
using min and range of the data set:
z= (x - min_x) / (max_x - min_x)
making the data to fall in to [0,1]
