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What do you mean by expected frequencies in chi-square test?
For a chi-square test there is a null hypothesis which describes some distribution for the variable that is being tested. The expected frequency for a particular cell is the number of observations that would be expected in that cell if the null hypothesis were true.
Distinguish between mean deviation and standard deviation?
The mean deviation for any distribution is always 0 and so conveys no information whatsoever. The standard deviation is the square root of the variance. The variance of a set of values is the sum of the probability of each value multiplied by the square of its difference from the mean for the set. A simpler way to calculate the variance is Expected value of squares - Square of Expected value.
How much error is expected between the sample mean and population mean?
0. The expected value of the sample mean is the population mean, so the expected value of the difference is 0.
Difference between mean and expected value?
For a population the mean and the expected value are just two names for the same thing. For a sample the mean is the same as the average and no expected value exists.
What will produce a large value for the chi-square statistic?
A chi-square statistic can be large if either there is a large difference between the observed and expected values for one or more categories. However, it can also be large if the expected value in a category is very small. In the first case, it is likely that the data are not distributed according to the null hypothesis. In the second case, it can often mean that that, because of low expected values, adjacent categories need to be combined before the chi-square statistic is calculated.
