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Q: In a data set the number of observations will always be the same as the number of what?
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When may the median of a set of data not be a member of the set data?

It can't * * * * * Yes it can. When there are an even number of observations and the middle two numbers are not the same.


Is the number of permutations of 2 items from the same data set always 2 times the number of combiations when taking 2 objects from a data set?

Yes


Is the number of permutations of two items from a data set is always two times the number of combinations when taking two objects at a time from the same data set?

Yes


What are quartiles in relationship to mean median mode?

Quartiles are values that divide a sample of data into four groups containing the same number of observations. You will find details in the related link.


Is it true that the score of the same data with the same mean are always the same?

No, it is not true.


How do you get class interval?

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.


How can you average averages?

-- Multiply the first averages by the number of observation for each set of these. -- Add up the sets of averages. -- Divide the sum by the total number of observations (Add cardinaility of each set). -- The result is the average of the averages. If you say have 4 "average" value and just add these, and divide by 4, the result is "unfair" because average may be of 3 observations, while another of 1000. So, to "compensate" and make every observation just as valuable, you re-generate the "sum of sums" and then divide by the total number of observations. If all sets are the same you can divide by number of observations.


Can the variance be a negative number?

First, we compute the variance by taking the sum of squares and divide that by N which is the number of data points in the same. It is average squared deviation of each number from its mean. The point is a squared number is always positive and N is always positive so the variance must always be non-negative. ( It can be 0). The variance is a measure of the dispersion of a set of data points around their mean value. It would not make sense for it to be negative.


Mode always equal to a value in the data set?

Yes.But only if the mode exists.If all the values in the dataset appear the same number of times there is no mode.


Is it possible for a coefficient of variation of a set of data to be zero Explain.?

Yes it is. If all the observations have the same non-zero value then the coefficient of variation will be zero.


Does every data set have a range?

Yes, unless all the data are the same number.


Element within a group always have the same number of?

Elements within a group always have the same number of valence electrons.