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how can one estimate the mean and variance of data that are summarized in a grouped...

how can one estimate the mean and variance of data that are summarized in a grouped frequency distribution? why are these only estimates?

Math   Statistics-And-Probability   
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Answer #1

Step 1: Determine the mid point (xi ) of each class interval

Step 2: Multiply these mid points (xi ) by the frequencies (fi ) of the corresponding classes

Step 3: The sum of the products divided by the total number of values is the mean of the data.

,

where

Variance (s2) of data that are summarized in a grouped frequency distribution is given by:

There are only estimates because these are calculated from sample only. These are estimates of the corresponding population mean () and population variance () respectively.

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