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I have recently began studying statistics with my learning material being a book on "Basic Statistics for the Behavioral Sciences"Sciences by Kenneth D. Hopkins and Gene V Glass (1978)", and so far I have understood concepts from the central measures of central tendencies (i.e. the mean, median, mode and rangemode) as well as the range to standard deviations. But when trying to tackle the exercises I have come across difficulties trying to understand the solutions.

One problem asks to estimate the separate ranges of three samples of 10, 100 and 1000 individuals involving height with a mean of 63.5 inches and a standard deviation of 2.5 inches. The distribution is normal. The answers were stated as follows using the equation ~ range = E*(standard deviation):

For n = 10, range = 3.1(2.5) = 7.75

For n = 100, range = 5(2.5) = 12.5

For n = 1000, range = 6.5(2.5) = 16.25

The issue I have is that I do not understand how the expected value, E, was calculated or why this equation works as a method for estimating the range. I would be much obliged if someone could explain this to me.

I have recently began studying statistics with my learning material being a book on "Basic Statistics for the Behavioral Sciences", and so far I have understood concepts from the central measures of tendencies (i.e. the mean, median, mode and range) to standard deviations. But when trying to tackle the exercises I have come across difficulties trying to understand the solutions.

One problem asks to estimate the separate ranges of three samples of 10, 100 and 1000 individuals involving height with a mean of 63.5 inches and a standard deviation of 2.5 inches. The answers were stated as follows using the equation ~ range = E*(standard deviation):

For n = 10, range = 3.1(2.5) = 7.75

For n = 100, range = 5(2.5) = 12.5

For n = 1000, range = 6.5(2.5) = 16.25

The issue I have is that I do not understand how the expected value, E, was calculated or why this equation works as a method for estimating the range. I would be much obliged if someone could explain this to me.

I have recently began studying statistics with my learning material being a book on "Basic Statistics for the Behavioral Sciences by Kenneth D. Hopkins and Gene V Glass (1978)", and so far I have understood concepts from the measures of central tendencies (i.e. the mean, median and mode) as well as the range to standard deviations. But when trying to tackle the exercises I have come across difficulties trying to understand the solutions.

One problem asks to estimate the separate ranges of three samples of 10, 100 and 1000 individuals involving height with a mean of 63.5 inches and a standard deviation of 2.5 inches. The distribution is normal. The answers were stated as follows using the equation ~ range = E*(standard deviation):

For n = 10, range = 3.1(2.5) = 7.75

For n = 100, range = 5(2.5) = 12.5

For n = 1000, range = 6.5(2.5) = 16.25

The issue I have is that I do not understand how the expected value, E, was calculated or why this equation works as a method for estimating the range. I would be much obliged if someone could explain this to me.

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The Contextual Path
The Contextual Path
  • 11
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Calculating Range based on Mean, Standard Deviation and Varying Sample Size

I have recently began studying statistics with my learning material being a book on "Basic Statistics for the Behavioral Sciences", and so far I have understood concepts from the central measures of tendencies (i.e. the mean, median, mode and range) to standard deviations. But when trying to tackle the exercises I have come across difficulties trying to understand the solutions.

One problem asks to estimate the separate ranges of three samples of 10, 100 and 1000 individuals involving height with a mean of 63.5 inches and a standard deviation of 2.5 inches. The answers were stated as follows using the equation ~ range = E*(standard deviation):

For n = 10, range = 3.1(2.5) = 7.75

For n = 100, range = 5(2.5) = 12.5

For n = 1000, range = 6.5(2.5) = 16.25

The issue I have is that I do not understand how the expected value, E, was calculated or why this equation works as a method for estimating the range. I would be much obliged if someone could explain this to me.