I have 3 arrays:
A1 = [1, 1, 1, 1, 5]
A2 = [1, 1, 1, 2, 4]
A3 = [1, 1, 2, 2, 3]
I want a parameter which would prefer A1 (an array having "more small values" even though total sums are almost equal) over rest arrays.
Before I thought of just adding all elements in an array then comparing all three of them. Then I realised this method will not work.
Note: The number 3 Arrays is just for illustration of my intensions. In actual scenario there could be 10000's of such arrays and I would to pick the best one using the suggested parameter's value.
In a technical sense 'parameter' refers to a property of a distribution and 'statistic' refers to a summary based on values in a sample.
I suppose you want a statistic that expresses the 'typical' value of each array. Frequently used statistics are the mean (total divided by sample size), median (middle value of sorted data; average of middle two if there the number of elements is even), and mode (most frequent value, if there is one)
For $A_i,$ the mean is 1.8, the median is 1, and there is a mode at 1.
For $A_2,$ the mean is 1.8, the median is 1, and there is a mode at 1.
For $A_3,$ the mean is 1.8, the median is 2, and there is no mode.
There are many other specialized statistics that measure 'location', some developed for special applications. A 20% trimmed mean might be of interest for your three arrays. To begin, 20% of the observations are removed from the low and high ends of the sorted data, respectively, and then the remaining observations (in your case, three of them) are averaged. For $A_1, A_2, A_3$ the 20% trimmed means are $1.000, 1.333, 1.667,$ respectively.
If you really want to focus on the smaller values, you might want to use one of the lower quantiles. The 40th percentile of an arrays of five elements would be the second highest of the sorted data: in your example, $1$ for each array. (Different software packages and different textbooks use slightly different definitions of quantiles.)
You need to try to clarify exactly what property of your arrays you want a statistic to express. Then you may be able to decide which statistic to use. With only your brief description to go on, I guess the median or the trimmed mean might be best.
Note: You gave examples with only five elements per array, so I used a 20% trimmed mean for an illustration. For larger arrays it might be better to use the more common 5% trimmed mean.