A dataset has 1000 records and 50 variables with 5% of the values miss

Question

A dataset has 1000 records and 50 variables with 5% of the values missing, spread randomly throughout the records and variables. An analyst decides to remove records that have missing values. About how many records would you expect would be removed?

No official solution - from and old probability text book.

beyondgmatscore · Answer

Since 5% of records have missing values, the expected value of number of missing record is 1000*5% = 50. This looks like an illustration of expected value of an outcome.

fluke · Answer

If a dataset has 1000 records and 50 variables;

It has 1000*50=50000 values

5% of 50000 = 2500 values are missing;

Maximum number of records that may contain these missing values = 1000 (If around 2.5 values missing from every record)
Minimum number of records that may contain these missing values = 2500/50 = 50 (if each of these 50 records contains missing values for all its variables)

So; the range is 50 records to be removed(best case scenario)->all 1000 records to be removed(worst case scenario)

Wonder how would you calculate probability out of this info!!!

beyondgmatscore · Answer

I think the question is phrased ambiguously. The data set has 1000 records and 50 variables - its unclear whether there are 1000 records for each of the 50 variables or that each variable has certain number of records and the total number of records in 1000.

fluke · Answer

A rephrasing of the question would be:

A table has 1000 rows and 50 columns with 5% of the values missing, spread randomly throughout the rows and columns. An analyst decides to remove rows that have missing values. About how many rows would you expect would be removed?

beyondgmatscore · Answer

Above rephrasing clarifies it better, but it would still leave the question incomplete, as in those 2500 values can be distributed across those 1000 rows in any number of ways.

IanStewart · Answer

This question is far, far beyond the scope of the GMAT. If you care about how to solve it (and if you're just studying for the GMAT, believe me, you don't care!) then you'd expect there to be on average 2.5 missing values per row. The probability of a missing value is .05, so using binomial probability, the standard deviation of the number of missing values per row is root(50*0.05*0.95) = 1.54 (approximately). You'd then need to consult a normal distribution stats table to figure out what percentage of rows you'd expect to have 0 incomplete entries (what percentage would be more than 2.5/1.54 = 1.6 standard deviations below the expected value). You don't have stats tables at hand during the GMAT, so you can't possibly answer this question on the GMAT, and the knowledge required is way beyond the test regardless.

As general advice, it's not a good idea to use, say, undergraduate probability or stats textbooks for GMAT preparation. You'll waste a lot of your time studying material that is entirely irrelevant to the test. Anyone preparing for the GMAT should ignore this thread.

As general advice, it's not a good idea to use, say, undergraduate probability or stats textbooks for GMAT preparation. You'll waste a lot of your time studying material that is entirely irrelevant to the test. Anyone preparing for the GMAT should ignore this thread.

beyondgmatscore · Answer

Ian - what you are saying would be true if we can assume these missing values are normally distributed - we don't have any such information in the question, so cant really assume a normal distribution - or can we?

IanStewart · Answer

This is all completely irrelevant for the GMAT, but for interest only: say you flip a coin 1000 times, and write down how many Heads you get. Then you repeat that experiment a million times, writing down a list of the numbers of Heads you get each time. Of course, on average you'll have 500 Heads, but the number of Heads in your list will be binomially (approximately normally) distributed. That's precisely where the normal distribution comes from; the normal distribution describes the distribution of the number of Heads you'll get when you flip a coin an infinite number of times. Whenever you have a sequence of independent events where each event has some fixed probability of 'success', you have a binomial distribution. So I wasn't making any assumptions (technically I was ignoring the slight dependence built into the question, but that shouldn't materially affect the answer). In any case, the normal distribution is *not* tested on the GMAT, so you don't need to know any of this.

sghaneka · Answer

Thanks so much for you advice. I was just curious looking at the problem.

Posted from my mobile device

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A dataset has 1000 records and 50 variables with 5% of the values miss

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