When data are summarised into classes, their exact values are lost. There is no way of knowing whether the original observations were near the bottom of the class, the top of the class or evenly spread out.
Assuming that all the observations that fall into a particular class take the midpoint value is a reasonable approximation. It is the maximum likelihood unbiased estimate. It also sets the variance within each class to 0.
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Because sometimes adjacent classes have to be merged so that the frequencies are not too small. This is important if anonymity is to be preserved. It is also important for statistical testing.
yes
They ARE important.
You don't GET class intervals. The person analysing the data chooses what class interval gives the best summary of the data. Ideally you are looking for class intervals that havea reasonable number of observations in each class (5 or more),a reasonable number of classes,(sometimes) observations within the same class are as similar to one another as possible while observations between classes are as different as possible (maximum discrimination),a nice round numbers as their midpoints.The first three are important for some kinds of statistical analyses. The last is to make calculations simpler and interpretation of the results easier.
perimeter and area. then again i am only in fourth grade gt class