Calculating percentile given z score
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What is the formula to convert a z-score to its appropriate percentile?
I have not found an answer on this site nor on Google. I assume there is a formula.
probability statistics
asked Dec 7 '18 at 2:07
JinzuJinzu
381413
$endgroup$
add a comment |
$begingroup$
What is the formula to convert a z-score to its appropriate percentile?
I have not found an answer on this site nor on Google. I assume there is a formula.
probability statistics
asked Dec 7 '18 at 2:07
JinzuJinzu
381413
$endgroup$
$begingroup$
You mean... the area?
$endgroup$
– Sean Roberson
Dec 7 '18 at 4:27
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If $X sim mathcal{N}(mu, sigma^2)$, then for a certain quantile $q$ and the corresponding z-score $z$ will satisfy $q = mu + sigma z$. If you are interested in the CDF $Pr{X leq q}$ instead, you will need a numerical method to compute that integral - either pre-computed table or statistical software.
$endgroup$
– BGM
Dec 7 '18 at 6:59
add a comment |
$begingroup$
What is the formula to convert a z-score to its appropriate percentile?
I have not found an answer on this site nor on Google. I assume there is a formula.
probability statistics
asked Dec 7 '18 at 2:07
JinzuJinzu
381413
$endgroup$
What is the formula to convert a z-score to its appropriate percentile?
I have not found an answer on this site nor on Google. I assume there is a formula.
probability statistics
probability statistics
asked Dec 7 '18 at 2:07
JinzuJinzu
381413
asked Dec 7 '18 at 2:07
JinzuJinzu
381413
asked Dec 7 '18 at 2:07
JinzuJinzu
381413
asked Dec 7 '18 at 2:07
JinzuJinzu
381413
asked Dec 7 '18 at 2:07
JinzuJinzu
381413
381413
$begingroup$
You mean... the area?
$endgroup$
– Sean Roberson
Dec 7 '18 at 4:27
$begingroup$
If $X sim mathcal{N}(mu, sigma^2)$, then for a certain quantile $q$ and the corresponding z-score $z$ will satisfy $q = mu + sigma z$. If you are interested in the CDF $Pr{X leq q}$ instead, you will need a numerical method to compute that integral - either pre-computed table or statistical software.
$endgroup$
– BGM
Dec 7 '18 at 6:59
add a comment |
$begingroup$
You mean... the area?
$endgroup$
– Sean Roberson
Dec 7 '18 at 4:27
$begingroup$
If $X sim mathcal{N}(mu, sigma^2)$, then for a certain quantile $q$ and the corresponding z-score $z$ will satisfy $q = mu + sigma z$. If you are interested in the CDF $Pr{X leq q}$ instead, you will need a numerical method to compute that integral - either pre-computed table or statistical software.
$endgroup$
– BGM
Dec 7 '18 at 6:59
$begingroup$
You mean... the area?
$endgroup$
– Sean Roberson
Dec 7 '18 at 4:27
$begingroup$
You mean... the area?
$endgroup$
– Sean Roberson
Dec 7 '18 at 4:27
$begingroup$
If $X sim mathcal{N}(mu, sigma^2)$, then for a certain quantile $q$ and the corresponding z-score $z$ will satisfy $q = mu + sigma z$. If you are interested in the CDF $Pr{X leq q}$ instead, you will need a numerical method to compute that integral - either pre-computed table or statistical software.
$endgroup$
– BGM
Dec 7 '18 at 6:59
$begingroup$
If $X sim mathcal{N}(mu, sigma^2)$, then for a certain quantile $q$ and the corresponding z-score $z$ will satisfy $q = mu + sigma z$. If you are interested in the CDF $Pr{X leq q}$ instead, you will need a numerical method to compute that integral - either pre-computed table or statistical software.
$endgroup$
– BGM
Dec 7 '18 at 6:59
add a comment |
1 Answer
1
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votes
$begingroup$
If $z$ is the $z$-score, then you get the corresponding percentile $p_z$ by
$$ p_z =left lceil {P(Z leq z)cdot 100 } right rceil$$
Here $left lceil x right rceil$ is the ceiling function $left lceil x right rceil = min {p in mathbb{Z}| p geq x }$ and $Z sim N(0,1)$.
For example, you may find $P(Z leq z)$ here for $z = 1.2$ using WolframAlpha and obtain that this score belongs to the $89^{mbox{th}}$ percentile.
answered Dec 7 '18 at 8:07
trancelocationtrancelocation
10.5k1722
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add a comment |
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1 Answer
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$begingroup$
If $z$ is the $z$-score, then you get the corresponding percentile $p_z$ by
$$ p_z =left lceil {P(Z leq z)cdot 100 } right rceil$$
Here $left lceil x right rceil$ is the ceiling function $left lceil x right rceil = min {p in mathbb{Z}| p geq x }$ and $Z sim N(0,1)$.
For example, you may find $P(Z leq z)$ here for $z = 1.2$ using WolframAlpha and obtain that this score belongs to the $89^{mbox{th}}$ percentile.
answered Dec 7 '18 at 8:07
trancelocationtrancelocation
10.5k1722
$endgroup$
add a comment |
$begingroup$
If $z$ is the $z$-score, then you get the corresponding percentile $p_z$ by
$$ p_z =left lceil {P(Z leq z)cdot 100 } right rceil$$
Here $left lceil x right rceil$ is the ceiling function $left lceil x right rceil = min {p in mathbb{Z}| p geq x }$ and $Z sim N(0,1)$.
For example, you may find $P(Z leq z)$ here for $z = 1.2$ using WolframAlpha and obtain that this score belongs to the $89^{mbox{th}}$ percentile.
answered Dec 7 '18 at 8:07
trancelocationtrancelocation
10.5k1722
$endgroup$
add a comment |
$begingroup$
If $z$ is the $z$-score, then you get the corresponding percentile $p_z$ by
$$ p_z =left lceil {P(Z leq z)cdot 100 } right rceil$$
Here $left lceil x right rceil$ is the ceiling function $left lceil x right rceil = min {p in mathbb{Z}| p geq x }$ and $Z sim N(0,1)$.
For example, you may find $P(Z leq z)$ here for $z = 1.2$ using WolframAlpha and obtain that this score belongs to the $89^{mbox{th}}$ percentile.
answered Dec 7 '18 at 8:07
trancelocationtrancelocation
10.5k1722
$endgroup$
If $z$ is the $z$-score, then you get the corresponding percentile $p_z$ by
$$ p_z =left lceil {P(Z leq z)cdot 100 } right rceil$$
Here $left lceil x right rceil$ is the ceiling function $left lceil x right rceil = min {p in mathbb{Z}| p geq x }$ and $Z sim N(0,1)$.
For example, you may find $P(Z leq z)$ here for $z = 1.2$ using WolframAlpha and obtain that this score belongs to the $89^{mbox{th}}$ percentile.
answered Dec 7 '18 at 8:07
trancelocationtrancelocation
10.5k1722
answered Dec 7 '18 at 8:07
trancelocationtrancelocation
10.5k1722
answered Dec 7 '18 at 8:07
trancelocationtrancelocation
10.5k1722
answered Dec 7 '18 at 8:07
trancelocationtrancelocation
10.5k1722
10.5k1722
add a comment |
add a comment |
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$begingroup$
You mean... the area?
$endgroup$
– Sean Roberson
Dec 7 '18 at 4:27
$begingroup$
If $X sim mathcal{N}(mu, sigma^2)$, then for a certain quantile $q$ and the corresponding z-score $z$ will satisfy $q = mu + sigma z$. If you are interested in the CDF $Pr{X leq q}$ instead, you will need a numerical method to compute that integral - either pre-computed table or statistical software.
$endgroup$
– BGM
Dec 7 '18 at 6:59