Issues with manipulating matrix transposed using bash script - arrays

Question

I wrote a bash script that is supposed to calculate the statistical average and median of each columns of an input file. The input file format is shown below. Each number is separated by a tab.
1 2 3
3 2 8
3 4 2
My approach is to first transpose the matrix, so that rows become columns and vice versa. The transposed matrix is stored in a temporary text file. Then, I calculated the average and median for rows. However, the script gives me the wrong output. First of all, the array that holds the average and median for each column only produces one output. Secondly, the median value calculated is incorrect.
After a bit of code inspection and testing, I discovered that while the transposed matrix did get written to the text file, it is not read correctly by the script. Specifically, each line read only gives one number. Below is my script.
#if column is chosen instead
89 if [[ $initial == "-c" ]]
90 then
91 echo "Calculating column stats"
92
93 #transpose columns to row to make life easier
94 WORD=$(head -n 1 $filename | wc -w); #counts the number of columns
95 for((index=1; index<=$WORD; index++)) #loop it over the number of columns
96 do
97 awk '{print $'$index'}' $filename | tr '\n' ' ';echo; #compact way of performing a row-col transposition
98 #prints the column as determined by $index, and then translates new-line with a tab
99 done > tmp.txt
100
101 array=()
102 averageArray=()
103 medianArray=()
104 sortedArray=()
105
106 #calculate average and median, just like the one used for rows
107 while read -a cols
108 do
109 total=0
110 sum=0
111
112 for number in "${cols[#]}" #for every item in the transposed column
113 do
114 (( sum += $number )) #the total sum of the numbers in the column
115 (( total++ )) #the number of items in the column
116 array+=( $number )
117 done
118
119 sortedArray=( $( printf "%s\n" "${array[#]}" | sort -n) )
120 arrayLength=${#sortedArray[#]}
121 #echo sorted array is $sortedArray
122 #based on array length, construct the median array
123 if [[ $(( arrayLength % 2 )) -eq 0 ]]
124 then #even
125 upper=$(( arrayLength / 2 ))
126 lower=$(( (arrayLength/2) - 1 ))
127 median=$(( (${sortedArray[lower]} + ${sortedArray[upper]}) / 2 ))
128 #echo median is $median
129 medianArray+=$index
130 else #odd
131 middle=$(( (arrayLength) / 2 ))
132 median=${sortedArray[middle]}
133 #echo median is $median
134 medianArray+=$index
135 fi
136 averageArray+=( $((sum/total)) ) #the final row array of averages that is displayed
137
138 done < tmp.txt
139 fi
Thanks for the help.