You have a dimension mismatch if (for example) you are doing 2-var stats and the two lists do not have the same length. You can also have mismatch with matrices.
SOURCE: TI-83 Plus Calculator: what does ERR: DIM MISMATCH mean?...
Imagine you are doing statistical calculations with two list, say L1 and L2 but one list has 10 elements (values) while the other has only 9. The dimension of the lists are different (mismatched) because one is 10 and the other 9.
Another case is if you are manipulating matrices such as adding a3x3 matrix to 3x2 matrix. Both matrices have the same number of rows but different numbers of columns.
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