Can You Have 2 Numerical, Identical Values To Represent the nth Percentile?












1














For an assignment, I am required to find the value of a piece of data in the 70th
percentile using mean and standard deviation.



Here is my organized data in ascending order: 0, 1, -4, 0, -3, 0, -4, -2, 0, 1, -1, 2, 0, -4, 5, -2, 0, 3, -3, 0.



The image link attached below called 'Percentiles With Normal Distribution' is the work I have done to find the value. (For some reason I can`t seem to upload the actual image here...)



Percentiles with Normal Distribution



Just in case you cannot access the image, I will explain what I did.




  1. I created the normal distribution graph and shaded approximately 70% of it, leaving a little part on the right side empty. I am finding b, where P(X > b) = p, where p = 0.7. I reversed this and it is now P(X > b) = 1 - p (where p = 0.7). This means to find the (1-p)Th percentile for X.


  2. Next, I found the corresponding percentile for Z by looking in the body of the Z-Score Table, and finding the probability that is closest to p = 0.7, to which I did this: (1-0.7) = 0.3 so the closest value to this is 0.3015, which falls under row = -0.5 and column = 0.02. This means the 70th percentile for Z is equal to -0.52.


  3. Lastly, I just changed the Z-Score value back into an x-value (original units). x = Mean + Z(Standard Deviation). I substiuted my mean value of -0.55, Z-Score value of -0.52, and standard deviation of 2.4 and solved for x. x = -2.



Now, if you look at the organized data set I provided above, youd see that there are two -2s. This is confusing me because I`m not sure whether there can be two numerical values to represent the value of a certain percentile.










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Yashvi Shah is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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    1














    For an assignment, I am required to find the value of a piece of data in the 70th
    percentile using mean and standard deviation.



    Here is my organized data in ascending order: 0, 1, -4, 0, -3, 0, -4, -2, 0, 1, -1, 2, 0, -4, 5, -2, 0, 3, -3, 0.



    The image link attached below called 'Percentiles With Normal Distribution' is the work I have done to find the value. (For some reason I can`t seem to upload the actual image here...)



    Percentiles with Normal Distribution



    Just in case you cannot access the image, I will explain what I did.




    1. I created the normal distribution graph and shaded approximately 70% of it, leaving a little part on the right side empty. I am finding b, where P(X > b) = p, where p = 0.7. I reversed this and it is now P(X > b) = 1 - p (where p = 0.7). This means to find the (1-p)Th percentile for X.


    2. Next, I found the corresponding percentile for Z by looking in the body of the Z-Score Table, and finding the probability that is closest to p = 0.7, to which I did this: (1-0.7) = 0.3 so the closest value to this is 0.3015, which falls under row = -0.5 and column = 0.02. This means the 70th percentile for Z is equal to -0.52.


    3. Lastly, I just changed the Z-Score value back into an x-value (original units). x = Mean + Z(Standard Deviation). I substiuted my mean value of -0.55, Z-Score value of -0.52, and standard deviation of 2.4 and solved for x. x = -2.



    Now, if you look at the organized data set I provided above, youd see that there are two -2s. This is confusing me because I`m not sure whether there can be two numerical values to represent the value of a certain percentile.










    share|cite|improve this question







    New contributor




    Yashvi Shah is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
    Check out our Code of Conduct.























      1












      1








      1







      For an assignment, I am required to find the value of a piece of data in the 70th
      percentile using mean and standard deviation.



      Here is my organized data in ascending order: 0, 1, -4, 0, -3, 0, -4, -2, 0, 1, -1, 2, 0, -4, 5, -2, 0, 3, -3, 0.



      The image link attached below called 'Percentiles With Normal Distribution' is the work I have done to find the value. (For some reason I can`t seem to upload the actual image here...)



      Percentiles with Normal Distribution



      Just in case you cannot access the image, I will explain what I did.




      1. I created the normal distribution graph and shaded approximately 70% of it, leaving a little part on the right side empty. I am finding b, where P(X > b) = p, where p = 0.7. I reversed this and it is now P(X > b) = 1 - p (where p = 0.7). This means to find the (1-p)Th percentile for X.


      2. Next, I found the corresponding percentile for Z by looking in the body of the Z-Score Table, and finding the probability that is closest to p = 0.7, to which I did this: (1-0.7) = 0.3 so the closest value to this is 0.3015, which falls under row = -0.5 and column = 0.02. This means the 70th percentile for Z is equal to -0.52.


      3. Lastly, I just changed the Z-Score value back into an x-value (original units). x = Mean + Z(Standard Deviation). I substiuted my mean value of -0.55, Z-Score value of -0.52, and standard deviation of 2.4 and solved for x. x = -2.



      Now, if you look at the organized data set I provided above, youd see that there are two -2s. This is confusing me because I`m not sure whether there can be two numerical values to represent the value of a certain percentile.










      share|cite|improve this question







      New contributor




      Yashvi Shah is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.











      For an assignment, I am required to find the value of a piece of data in the 70th
      percentile using mean and standard deviation.



      Here is my organized data in ascending order: 0, 1, -4, 0, -3, 0, -4, -2, 0, 1, -1, 2, 0, -4, 5, -2, 0, 3, -3, 0.



      The image link attached below called 'Percentiles With Normal Distribution' is the work I have done to find the value. (For some reason I can`t seem to upload the actual image here...)



      Percentiles with Normal Distribution



      Just in case you cannot access the image, I will explain what I did.




      1. I created the normal distribution graph and shaded approximately 70% of it, leaving a little part on the right side empty. I am finding b, where P(X > b) = p, where p = 0.7. I reversed this and it is now P(X > b) = 1 - p (where p = 0.7). This means to find the (1-p)Th percentile for X.


      2. Next, I found the corresponding percentile for Z by looking in the body of the Z-Score Table, and finding the probability that is closest to p = 0.7, to which I did this: (1-0.7) = 0.3 so the closest value to this is 0.3015, which falls under row = -0.5 and column = 0.02. This means the 70th percentile for Z is equal to -0.52.


      3. Lastly, I just changed the Z-Score value back into an x-value (original units). x = Mean + Z(Standard Deviation). I substiuted my mean value of -0.55, Z-Score value of -0.52, and standard deviation of 2.4 and solved for x. x = -2.



      Now, if you look at the organized data set I provided above, youd see that there are two -2s. This is confusing me because I`m not sure whether there can be two numerical values to represent the value of a certain percentile.







      probability normal-distribution standard-deviation percentile






      share|cite|improve this question







      New contributor




      Yashvi Shah is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.











      share|cite|improve this question







      New contributor




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      Check out our Code of Conduct.









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      asked Jan 3 at 21:34









      Yashvi Shah

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      New contributor




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      New contributor





      Yashvi Shah is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.






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      Check out our Code of Conduct.






















          1 Answer
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          0














          Three points:




          1. If you look at your picture, you want $+0.52$ for the $70$th percentile of a standard normal distribution, but you used $-0.52$ which in fact corresponds to the $30$th percentile. Correcting this would have given you about $0.7$ rather than $-1.8$


          2. There is no problem with a percentile corresponding to a value from the sample which happens multiple times. For example with the data 3, 5, 5, 5, 7 it is obvious that the $50$th percentile or median is $5$


          3. I am not sure why you need to fit a normal distribution unless it is to fit the question's "using mean and standard deviation". As an alternative, sorting your $20$ data points to -4, -4, -4, -3, -3, -2, -2, -1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 3, 5, you have $25%$ of the values below $-2$ and $65%$ of the values above $-2$ so you could say $-2$ is the $30$th percentile. Similarly you have $40%$ of the values below $0$ and $25%$ above $0$ so you could say $0$ is the $70$th percentile.



          enter image description here






          share|cite|improve this answer























          • This really helps! Thank you! But, is there a mathematical calculation way to prove that 0 is the 70th percentile? My teacher demands mathematical calculations. The way I’ve done it, I’m getting -2.
            – Yashvi Shah
            2 days ago










          • @YashviShah: all my comments were mathematical. You should not be getting $-2$ but about $0.7$ from your calculations.
            – Henry
            2 days ago










          • To justify $0$ you could draw an empirical cumulative distribution graph perhaps like the one I have added to my answer
            – Henry
            2 days ago










          • Im not quite sure how youre getting 0 as the 70th percentile through the calculations. Did you calculate the same way I did up there? What did you do? Im trying to get the result of 0 being the 70th percentile. And as for the empirical cumulative distribution graph, I dont think we learnt that. Is there a way to justify using a normal distribution graph or something?
            – Yashvi Shah
            2 days ago










          • Also, I used this link to help me with getting the percentile value using mean and standard deviation - dummies.com/education/math/statistics/…
            – Yashvi Shah
            2 days ago











          Your Answer





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          1 Answer
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          1 Answer
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          active

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          active

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          0














          Three points:




          1. If you look at your picture, you want $+0.52$ for the $70$th percentile of a standard normal distribution, but you used $-0.52$ which in fact corresponds to the $30$th percentile. Correcting this would have given you about $0.7$ rather than $-1.8$


          2. There is no problem with a percentile corresponding to a value from the sample which happens multiple times. For example with the data 3, 5, 5, 5, 7 it is obvious that the $50$th percentile or median is $5$


          3. I am not sure why you need to fit a normal distribution unless it is to fit the question's "using mean and standard deviation". As an alternative, sorting your $20$ data points to -4, -4, -4, -3, -3, -2, -2, -1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 3, 5, you have $25%$ of the values below $-2$ and $65%$ of the values above $-2$ so you could say $-2$ is the $30$th percentile. Similarly you have $40%$ of the values below $0$ and $25%$ above $0$ so you could say $0$ is the $70$th percentile.



          enter image description here






          share|cite|improve this answer























          • This really helps! Thank you! But, is there a mathematical calculation way to prove that 0 is the 70th percentile? My teacher demands mathematical calculations. The way I’ve done it, I’m getting -2.
            – Yashvi Shah
            2 days ago










          • @YashviShah: all my comments were mathematical. You should not be getting $-2$ but about $0.7$ from your calculations.
            – Henry
            2 days ago










          • To justify $0$ you could draw an empirical cumulative distribution graph perhaps like the one I have added to my answer
            – Henry
            2 days ago










          • Im not quite sure how youre getting 0 as the 70th percentile through the calculations. Did you calculate the same way I did up there? What did you do? Im trying to get the result of 0 being the 70th percentile. And as for the empirical cumulative distribution graph, I dont think we learnt that. Is there a way to justify using a normal distribution graph or something?
            – Yashvi Shah
            2 days ago










          • Also, I used this link to help me with getting the percentile value using mean and standard deviation - dummies.com/education/math/statistics/…
            – Yashvi Shah
            2 days ago
















          0














          Three points:




          1. If you look at your picture, you want $+0.52$ for the $70$th percentile of a standard normal distribution, but you used $-0.52$ which in fact corresponds to the $30$th percentile. Correcting this would have given you about $0.7$ rather than $-1.8$


          2. There is no problem with a percentile corresponding to a value from the sample which happens multiple times. For example with the data 3, 5, 5, 5, 7 it is obvious that the $50$th percentile or median is $5$


          3. I am not sure why you need to fit a normal distribution unless it is to fit the question's "using mean and standard deviation". As an alternative, sorting your $20$ data points to -4, -4, -4, -3, -3, -2, -2, -1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 3, 5, you have $25%$ of the values below $-2$ and $65%$ of the values above $-2$ so you could say $-2$ is the $30$th percentile. Similarly you have $40%$ of the values below $0$ and $25%$ above $0$ so you could say $0$ is the $70$th percentile.



          enter image description here






          share|cite|improve this answer























          • This really helps! Thank you! But, is there a mathematical calculation way to prove that 0 is the 70th percentile? My teacher demands mathematical calculations. The way I’ve done it, I’m getting -2.
            – Yashvi Shah
            2 days ago










          • @YashviShah: all my comments were mathematical. You should not be getting $-2$ but about $0.7$ from your calculations.
            – Henry
            2 days ago










          • To justify $0$ you could draw an empirical cumulative distribution graph perhaps like the one I have added to my answer
            – Henry
            2 days ago










          • Im not quite sure how youre getting 0 as the 70th percentile through the calculations. Did you calculate the same way I did up there? What did you do? Im trying to get the result of 0 being the 70th percentile. And as for the empirical cumulative distribution graph, I dont think we learnt that. Is there a way to justify using a normal distribution graph or something?
            – Yashvi Shah
            2 days ago










          • Also, I used this link to help me with getting the percentile value using mean and standard deviation - dummies.com/education/math/statistics/…
            – Yashvi Shah
            2 days ago














          0












          0








          0






          Three points:




          1. If you look at your picture, you want $+0.52$ for the $70$th percentile of a standard normal distribution, but you used $-0.52$ which in fact corresponds to the $30$th percentile. Correcting this would have given you about $0.7$ rather than $-1.8$


          2. There is no problem with a percentile corresponding to a value from the sample which happens multiple times. For example with the data 3, 5, 5, 5, 7 it is obvious that the $50$th percentile or median is $5$


          3. I am not sure why you need to fit a normal distribution unless it is to fit the question's "using mean and standard deviation". As an alternative, sorting your $20$ data points to -4, -4, -4, -3, -3, -2, -2, -1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 3, 5, you have $25%$ of the values below $-2$ and $65%$ of the values above $-2$ so you could say $-2$ is the $30$th percentile. Similarly you have $40%$ of the values below $0$ and $25%$ above $0$ so you could say $0$ is the $70$th percentile.



          enter image description here






          share|cite|improve this answer














          Three points:




          1. If you look at your picture, you want $+0.52$ for the $70$th percentile of a standard normal distribution, but you used $-0.52$ which in fact corresponds to the $30$th percentile. Correcting this would have given you about $0.7$ rather than $-1.8$


          2. There is no problem with a percentile corresponding to a value from the sample which happens multiple times. For example with the data 3, 5, 5, 5, 7 it is obvious that the $50$th percentile or median is $5$


          3. I am not sure why you need to fit a normal distribution unless it is to fit the question's "using mean and standard deviation". As an alternative, sorting your $20$ data points to -4, -4, -4, -3, -3, -2, -2, -1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 3, 5, you have $25%$ of the values below $-2$ and $65%$ of the values above $-2$ so you could say $-2$ is the $30$th percentile. Similarly you have $40%$ of the values below $0$ and $25%$ above $0$ so you could say $0$ is the $70$th percentile.



          enter image description here







          share|cite|improve this answer














          share|cite|improve this answer



          share|cite|improve this answer








          edited 2 days ago

























          answered Jan 3 at 22:32









          Henry

          98.4k475162




          98.4k475162












          • This really helps! Thank you! But, is there a mathematical calculation way to prove that 0 is the 70th percentile? My teacher demands mathematical calculations. The way I’ve done it, I’m getting -2.
            – Yashvi Shah
            2 days ago










          • @YashviShah: all my comments were mathematical. You should not be getting $-2$ but about $0.7$ from your calculations.
            – Henry
            2 days ago










          • To justify $0$ you could draw an empirical cumulative distribution graph perhaps like the one I have added to my answer
            – Henry
            2 days ago










          • Im not quite sure how youre getting 0 as the 70th percentile through the calculations. Did you calculate the same way I did up there? What did you do? Im trying to get the result of 0 being the 70th percentile. And as for the empirical cumulative distribution graph, I dont think we learnt that. Is there a way to justify using a normal distribution graph or something?
            – Yashvi Shah
            2 days ago










          • Also, I used this link to help me with getting the percentile value using mean and standard deviation - dummies.com/education/math/statistics/…
            – Yashvi Shah
            2 days ago


















          • This really helps! Thank you! But, is there a mathematical calculation way to prove that 0 is the 70th percentile? My teacher demands mathematical calculations. The way I’ve done it, I’m getting -2.
            – Yashvi Shah
            2 days ago










          • @YashviShah: all my comments were mathematical. You should not be getting $-2$ but about $0.7$ from your calculations.
            – Henry
            2 days ago










          • To justify $0$ you could draw an empirical cumulative distribution graph perhaps like the one I have added to my answer
            – Henry
            2 days ago










          • Im not quite sure how youre getting 0 as the 70th percentile through the calculations. Did you calculate the same way I did up there? What did you do? Im trying to get the result of 0 being the 70th percentile. And as for the empirical cumulative distribution graph, I dont think we learnt that. Is there a way to justify using a normal distribution graph or something?
            – Yashvi Shah
            2 days ago










          • Also, I used this link to help me with getting the percentile value using mean and standard deviation - dummies.com/education/math/statistics/…
            – Yashvi Shah
            2 days ago
















          This really helps! Thank you! But, is there a mathematical calculation way to prove that 0 is the 70th percentile? My teacher demands mathematical calculations. The way I’ve done it, I’m getting -2.
          – Yashvi Shah
          2 days ago




          This really helps! Thank you! But, is there a mathematical calculation way to prove that 0 is the 70th percentile? My teacher demands mathematical calculations. The way I’ve done it, I’m getting -2.
          – Yashvi Shah
          2 days ago












          @YashviShah: all my comments were mathematical. You should not be getting $-2$ but about $0.7$ from your calculations.
          – Henry
          2 days ago




          @YashviShah: all my comments were mathematical. You should not be getting $-2$ but about $0.7$ from your calculations.
          – Henry
          2 days ago












          To justify $0$ you could draw an empirical cumulative distribution graph perhaps like the one I have added to my answer
          – Henry
          2 days ago




          To justify $0$ you could draw an empirical cumulative distribution graph perhaps like the one I have added to my answer
          – Henry
          2 days ago












          Im not quite sure how youre getting 0 as the 70th percentile through the calculations. Did you calculate the same way I did up there? What did you do? Im trying to get the result of 0 being the 70th percentile. And as for the empirical cumulative distribution graph, I dont think we learnt that. Is there a way to justify using a normal distribution graph or something?
          – Yashvi Shah
          2 days ago




          Im not quite sure how youre getting 0 as the 70th percentile through the calculations. Did you calculate the same way I did up there? What did you do? Im trying to get the result of 0 being the 70th percentile. And as for the empirical cumulative distribution graph, I dont think we learnt that. Is there a way to justify using a normal distribution graph or something?
          – Yashvi Shah
          2 days ago












          Also, I used this link to help me with getting the percentile value using mean and standard deviation - dummies.com/education/math/statistics/…
          – Yashvi Shah
          2 days ago




          Also, I used this link to help me with getting the percentile value using mean and standard deviation - dummies.com/education/math/statistics/…
          – Yashvi Shah
          2 days ago










          Yashvi Shah is a new contributor. Be nice, and check out our Code of Conduct.










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