To find the mean of the table
20-30: 4, 30-40: 8, 40-50: 12, 50-60: 10, 60-70: 6
a student used the LOWER limit of each class as $x_i$ instead of the class mark. His answer will be:

With class marks 25, 35, 45, 55, 65 the correct $\sum f_i{x}_i=1860$ over $\sum f_i=40$, so the mean is 46.5. Every lower limit is exactly $\frac{h}{2}=5$ below its class mark, so every $x_i$ drops by 5 and the mean drops by exactly 5, to 41.5. It is a shift down, not up, and the size of the error is $h/2=5$, not $h=10$; the frequencies being unchanged does not protect the mean, because it is the $x_i$ that were wrong.