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**furor celtica** The standardised marks received by 318 students who took a mechanics examinations are summarised in the following grouped frequency table.

Mark 0-29 30-39 40-49 50-59 60-69 70-79 80-89 90-100

Frequency 12 7 13 25 46 78 105 32

I’m supposed to find the mean of these data, which should be fairly straightforward: sigma(xf)/sigma(f) taking mid-class values for x: 15, 35, 45, 55, 65, 75, 85, 95

So the mean = (15x12 + 35x7 + 45x13 + 55x25 + 65x46 + 75x78 + 85x105 + 95x32)/(318) = 72.9 to 3 s.f.

But the answer is 72.5, and I really don’t understand how to get there. Does this have something to do with conventional class boundaries, such as -0.5 to 29.5 for marks 0-29, 89.5 to 100.5 for marks 90-100, etc.? But I thought these were just for convention, I don’t see how they could alter the mean. Any hints would be appreciated

Sorry if this is unnecessarily detailed btw