The fastest way to find one unique value when all other values are the same
Benchmarks!
Benchmarks for lists with a thousand or a million elements, with the unique element in the middle of the array to reflect the &quot;typical&quot;/&quot;average&quot; case. The results are times, so lower=faster.
n=1000
0.90 find_uniq_Jacques
1.18 find_uniq_tinstaafl_1
0.59 find_uniq_tinstaafl_2
0.88 find_uniq_GZ0_1
0.14 find_uniq_GZ0_2
0.88 find_uniq_Peilonrayz
0.22 find_uniq_RootTwo
0.26 find_uniq_HeapOverflow_1
0.28 find_uniq_HeapOverflow_2
0.26 find_uniq_HeapOverflow_3
0.09 find_uniq_HeapOverFlow_Codewars
0.06 find_uniq_HeapOverflow_GZ0
0.57 unique_different_ethiy
0.28 find_uniq_KyleG_1
0.25 find_uniq_KyleG_2

n=1000000
0.94 find_uniq_Jacques
1.36 find_uniq_tinstaafl_1
0.68 find_uniq_tinstaafl_2
0.99 find_uniq_GZ0_1
0.19 find_uniq_GZ0_2
0.98 find_uniq_Peilonrayz
0.19 find_uniq_RootTwo
0.23 find_uniq_HeapOverflow_1
0.26 find_uniq_HeapOverflow_2
0.25 find_uniq_HeapOverflow_3
0.09 find_uniq_HeapOverFlow_Codewars
0.04 find_uniq_HeapOverflow_GZ0
0.57 unique_different_ethiy
0.28 find_uniq_KyleG_1
0.22 find_uniq_KyleG_2

Done with Python 3.8.1 32 bit on Windows 10 64 bit.
Benchmark code:
from timeit import timeit
from collections import Counter
from itertools import groupby

solutions = []
def register(solution):
    solutions.append(solution)
    return solution

@register
def find_uniq_Jacques(arr):
    nums = list(Counter(arr).items())
    data = [i for i in nums if i[1] == 1]
    return data[0][0]

@register
def find_uniq_tinstaafl_1(arr):
    for i in range(len(arr)-1):
        if arr[i] != arr[i+1]:
            if i == 0 and arr[i] != arr[i + 2]:
                return arr[i]
            return arr[i + 1]

@register
def find_uniq_tinstaafl_2(arr):
    for i in range(0,len(arr) - 1, 2):
        if arr[i] != arr[i+1]:
            if i == 0:
                if arr[i] != arr[i + 2]:
                    return arr[i]
                return arr[i + 1]
            else:
                if arr[i] != arr[i-1]:
                    return arr[i]
                return arr[i + 1]
    return arr[-1]

@register
def find_uniq_GZ0_1(arr):
    return next(k for k, freq in Counter(arr).items() if freq == 1)

@register
def find_uniq_GZ0_2(arr):
    group_iter = groupby(arr)
    k1, g1 = next(group_iter)
    c1 = len(list(g1))
    k2, g2 = next(group_iter)
    if c1 &gt; 1:
       # Group g1 has more than one element
       return k2
    try:
       # Group g2 has more than one element
       next(g2)
       next(g2)
       return k1
    except StopIteration:
       # Both g1 and g2 has one element
       return k2 if next(group_iter)[0] == k1 else k1

@register
def find_uniq_Peilonrayz(arr):
    return Counter(arr).most_common()[-1][0]

@register
def find_uniq_RootTwo(arr):
    a, b = set(arr)
    return a if arr[:3].count(a) &lt; 2 else b

@register
def find_uniq_HeapOverflow_1(arr):
    a = arr[0]
    if a not in arr[1:3]:
        return a
    for b in arr:
        if b != a:
            return b

@register
def find_uniq_HeapOverflow_2(arr):
    dupe = sorted(arr[:3])[1]
    for x in arr:
        if x != dupe:
            return x

@register
def find_uniq_HeapOverflow_3(arr):
    a = arr[0]
    for b in arr:
        if b != a:
            return b if a in arr[1:3] else a

@register
def find_uniq_HeapOverFlow_Codewars(arr):
    arr.sort()
    return arr[-(arr[0] == arr[1])]

@register
def find_uniq_HeapOverflow_GZ0(arr):
    group_iter = groupby(arr)
    k1, _ = next(group_iter)
    k2, g2 = next(group_iter)
    next(g2)
    return k1 if k2 in g2 else k2

@register
def unique_different_ethiy(iterable):
    # assert isinstance(iterable, Iterable)
    # assert len(iterable) &gt; 2
    if iterable[0] != iterable[1]:
        return iterable[0] if iterable[1] == iterable[2] else iterable[1]
    else:
        for element in iterable[2:]:
            if element != iterable[1]:
                return element

@register
def find_uniq_KyleG_1(arr):
    common = arr[0]
    if common not in arr[1:3]:
        return common
    for a, b in zip(arr[1::2], arr[2::2]):
        if a != b:
            if a == common:
                return b
            else:
                return a
    return arr[-1]

@register
def find_uniq_KyleG_2(arr):
    iterator = iter(arr)
    common = next(iterator)
    if common not in arr[1:3]:
        return common
    for a, b in zip(iterator, iterator):
        if a != b:
            if a == common:
                return b
            else:
                return a
    return arr[-1]

# Run the benchmarks
for e in 3, 6:
    n = 10**e
    number = 10**(7 - e)  # fewer number of runs for larger n
    print(f'{n=}')
    arr = [0] * n
    arr[n // 2] = 1

    # Repeat round-robin to reduce effects of CPU speed changes etc
    timeses = [[] for _ in solutions]
    for i in range(20):
        for solution, times in zip(solutions, timeses):
            arrs = iter([arr[:] for _ in range(number)])
            t = timeit(lambda: solution(next(arrs)), number=number)
            times.append(t)
        print(i, end=' ')
    print()
    for solution, times in zip(solutions, timeses):
        print('%.2f' % min(times), solution.__name__)
    print()