If two sets of data have the same range and same mean, then they have the same mode. determine whether this statement i sometimes, always. or never. provide evidence.

Sometimes true. This deals with the definition of range, mean, and mode. Range = difference between the smallest and largest number Mean = average. Just add up all the numbers together and divide by the number of numbers in the list. Mode = The number that occurs the most frequently. Now for an example where two lists of numbers that have the same range and mean, but don't have the same mode list_1 = {1, 2, 3, 3, 4, 5, 6, 7, 8, 9, 10} range = 9 mean = 5.27 mode = 3 list_2 = {1, 2, 3, 4, 4, 4, 6, 7, 8, 9, 10} range = 9 mean = 5.27 mode = 4 So the above 2 lists show a case where the range and mean match exactly, but they don't have the same mode. Now for two different lists where their mode does match. list_1 = {1, 2, 3, 3, 4, 5, 6, 7, 8, 9, 10} Range = 9 Mean = 5.27 Mode = 3 list_2 = {1, 2, 3, 3, 3, 4, 5, 8, 9, 10, 10} Range = 9 Mean = 5.27 Mode = 3 So as you can see, a 2 sets of data may have the same same and same mean and will only sometimes have the same mode.