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.
