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Why find the inflection points on a bell curve?

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0

$begingroup$

I understand that the inflection points on a standard normal curve can be calculated with the equation
$mu pm sigma$, or essentially where z = $pm$1.

I don't fully understand the significance of this in statistics.

My best guess so far is that they kind of represent barriers between data points whose speed at which they change percentile is slow versus fast. So, data points to the left of the first inflection point (where z < -1 and where the curve is convex) might at first change percentiles slowly, but then change more quickly over time. Between the two inflection points (where -1 < z < 1 and where the curve is concave), percentiles change quickly but pretty consistently.

Is this correct? Can knowing the inflection points help you better understand the data?

Thanks!

statistics normal-distribution descriptive-statistics

share|cite|improve this question

asked Mar 21 at 19:17

ejw0208ejw0208

61

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  The inflection points of the bell curve represents the point where the change of the slope changes from positive (negative) to negative (positive).
  $endgroup$
  – callculus
  Mar 21 at 19:33
  
  

  
  
  
  

add a comment | 

0

$begingroup$

I understand that the inflection points on a standard normal curve can be calculated with the equation
$mu pm sigma$, or essentially where z = $pm$1.

I don't fully understand the significance of this in statistics.

My best guess so far is that they kind of represent barriers between data points whose speed at which they change percentile is slow versus fast. So, data points to the left of the first inflection point (where z < -1 and where the curve is convex) might at first change percentiles slowly, but then change more quickly over time. Between the two inflection points (where -1 < z < 1 and where the curve is concave), percentiles change quickly but pretty consistently.

Is this correct? Can knowing the inflection points help you better understand the data?

Thanks!

statistics normal-distribution descriptive-statistics

share|cite|improve this question

asked Mar 21 at 19:17

ejw0208ejw0208

61

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  The inflection points of the bell curve represents the point where the change of the slope changes from positive (negative) to negative (positive).
  $endgroup$
  – callculus
  Mar 21 at 19:33
  
  

  
  
  
  

add a comment | 

$begingroup$

I understand that the inflection points on a standard normal curve can be calculated with the equation
$mu pm sigma$, or essentially where z = $pm$1.

I don't fully understand the significance of this in statistics.

My best guess so far is that they kind of represent barriers between data points whose speed at which they change percentile is slow versus fast. So, data points to the left of the first inflection point (where z < -1 and where the curve is convex) might at first change percentiles slowly, but then change more quickly over time. Between the two inflection points (where -1 < z < 1 and where the curve is concave), percentiles change quickly but pretty consistently.

Is this correct? Can knowing the inflection points help you better understand the data?

Thanks!

statistics normal-distribution descriptive-statistics

share|cite|improve this question

asked Mar 21 at 19:17

ejw0208ejw0208

61

$endgroup$

share|cite|improve this question

asked Mar 21 at 19:17

ejw0208ejw0208

61

share|cite|improve this question

asked Mar 21 at 19:17

ejw0208ejw0208

61

asked Mar 21 at 19:17

ejw0208ejw0208

61

asked Mar 21 at 19:17

ejw0208ejw0208

61