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I was reading an article about using the CDF to calculate the area between 2 points on the normal curve. They gave a sample of 7 for illustration purposes:

-4.0,-3.0,0.8,1.8,3.9,6.2,6.5

From this sample, the sample mean is 1.743, the SD = 4.154 , n=7

Then it says that given this information and assuming the sample was normally distributed, the sample would have the following characteristics 

expected sample values    CDF at each sample point    z score at sample point
-4.343                             1/14                      -1.465
-1.545                             3/14                      -0.792
 0.222                             5/14                      -0.366
 1.743                             1/2                        0.000
 3.264                             9/14                       0.366
 5.031                             11/14                      0.792
 7.829                             13/14                      1.465

Please would somebody kindly explain how the fractions would have been calculated? the sample is 7, so where did 14 come from etc. The text clearly explains how the Z scores were calculated (NORMSINV at the sample point) and the expected values (NORMINV) but I couldn't understand the fractions for CDF at each sample point.

Kind regards Dec

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  • $\begingroup$ So in the meantime, i've figured out how to get the CDF values. simply order and number (i) the data in ascending order. . Calculate (i-0.5)/n for each value; this represents the cumulative probability. So for the first value,(1-0.5)/7 = 0.071429, which is equivalent to the fraction 1/14. But how does one get that denominator? I would not want to work out the fraction by trial and error if you know what I mean.. $\endgroup$
    – user3497385
    Commented Aug 22, 2016 at 14:48
  • $\begingroup$ Looks like I'm going to have to answer my own question. Can't wait all day for you. that's for sure. So, what you do, after you have calculated the CDF values, right click the value in excel, click "format cells". Under the number tab, click 'fraction' and select "up to three digits'. It will then give you the fractions instead of the cumulative probabilities. $\endgroup$
    – user3497385
    Commented Aug 23, 2016 at 17:00
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    $\begingroup$ (1-0.5)/7 = (1/2)/7 = 1/(2*7) = 1/14 $\endgroup$
    – einar
    Commented Aug 24, 2016 at 6:15
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    $\begingroup$ Also more generally: (i-1/2)/7 = (2i -1)/14 (just multiply both numerator and denominator by 2) $\endgroup$
    – einar
    Commented Aug 24, 2016 at 7:50

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