not understanding how you do this could you explain please!

Question

The following table presents the time taken to review articles that were submitted for publication to the journal Technometrics during a recent year. A few articles took longer than 9 months to review; these are omitted from the table. Consider the data to be a population.

Time

0.0–0.9 45

1.0–1.9 17

2.0–2.9 18

3.0–3.9 19

4.0–4.9 12

5.0–5.9 14

6.0–6.9 13

7.0–7.9 22

8.0–8.9 11

Answer 1

mode = less than 1 month

median = 3 to 3.9 months

mean = the weighted average < median as it's skewed left, unless you count the ouliers at the right end

Answer 2

There's no question here. If you are trying to approximate the mean and standard deviation, you would normally just take the middle value of each sub-interval to use as the data values for that sub-intervval. This should be a reasonable guess if the data is scattered randomly across each sub-interval, as some would be less than the middle, and about the same number would be greater. It is an estimate, but the best we can do with the given information.

For example, to find the mean, we'd use [45*(0.9-0.0)/2 + 17*(1.9-1.0)/2 + ... + 11*(8.9-8.0)/2 ] / (45+17+...+11).