Which average would make the most sense (mean, mode, median)?
$begingroup$
I have musical data, for tuning information for notes of an instrument.
For each note played, I have the cents away from in tune (-50.0 - 50.0). I'd like to display the average each note was out of tune. I'm not sure which would make the most sense (eg. mean, mode, median) for this scenario.
Any tips for determining the best solution? The goal is to inform the user what their tuning tendencies are. Is there something else I should be using instead of the above options?
average
asked Dec 5 '18 at 23:19
user1218464user1218464
1083
$endgroup$
add a comment |
$begingroup$
I have musical data, for tuning information for notes of an instrument.
For each note played, I have the cents away from in tune (-50.0 - 50.0). I'd like to display the average each note was out of tune. I'm not sure which would make the most sense (eg. mean, mode, median) for this scenario.
Any tips for determining the best solution? The goal is to inform the user what their tuning tendencies are. Is there something else I should be using instead of the above options?
average
asked Dec 5 '18 at 23:19
user1218464user1218464
1083
$endgroup$
$begingroup$
It depends on whether you want to indicate that they have bias (e.g. they generally tend to tune to too high a pitch, or generally too low) or dispersion (they are not very good at getting the correct pitch).
$endgroup$
– Henry
Dec 5 '18 at 23:27
add a comment |
$begingroup$
I have musical data, for tuning information for notes of an instrument.
For each note played, I have the cents away from in tune (-50.0 - 50.0). I'd like to display the average each note was out of tune. I'm not sure which would make the most sense (eg. mean, mode, median) for this scenario.
Any tips for determining the best solution? The goal is to inform the user what their tuning tendencies are. Is there something else I should be using instead of the above options?
average
asked Dec 5 '18 at 23:19
user1218464user1218464
1083
$endgroup$
I have musical data, for tuning information for notes of an instrument.
For each note played, I have the cents away from in tune (-50.0 - 50.0). I'd like to display the average each note was out of tune. I'm not sure which would make the most sense (eg. mean, mode, median) for this scenario.
Any tips for determining the best solution? The goal is to inform the user what their tuning tendencies are. Is there something else I should be using instead of the above options?
average
average
asked Dec 5 '18 at 23:19
user1218464user1218464
1083
asked Dec 5 '18 at 23:19
user1218464user1218464
1083
asked Dec 5 '18 at 23:19
user1218464user1218464
1083
asked Dec 5 '18 at 23:19
user1218464user1218464
1083
asked Dec 5 '18 at 23:19
user1218464user1218464
1083
1083
$begingroup$
It depends on whether you want to indicate that they have bias (e.g. they generally tend to tune to too high a pitch, or generally too low) or dispersion (they are not very good at getting the correct pitch).
$endgroup$
– Henry
Dec 5 '18 at 23:27
add a comment |
$begingroup$
It depends on whether you want to indicate that they have bias (e.g. they generally tend to tune to too high a pitch, or generally too low) or dispersion (they are not very good at getting the correct pitch).
$endgroup$
– Henry
Dec 5 '18 at 23:27
$begingroup$
It depends on whether you want to indicate that they have bias (e.g. they generally tend to tune to too high a pitch, or generally too low) or dispersion (they are not very good at getting the correct pitch).
$endgroup$
– Henry
Dec 5 '18 at 23:27
$begingroup$
It depends on whether you want to indicate that they have bias (e.g. they generally tend to tune to too high a pitch, or generally too low) or dispersion (they are not very good at getting the correct pitch).
$endgroup$
– Henry
Dec 5 '18 at 23:27
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
I'm not sure that there is a mathematical answer to this question, as each statistic has their use. But, for what it is worth, here is my opinion on each three:
1) Tried and true, the mean is what people think of when they hear the word "average". Not a lot can go wrong with this statistic unless someone adds a note so severely out of tune that it isn't even the right note anymore.
2) Mode is almost certainly useless for you unless you plan on "bucketing" your results into small cent intervals, and even then you would do better to provide the entire histogram rather than just the mode.
3) The median is an excellent way of providing midpoint data, and it will help suppress outliers. I think it is fair to say, in general, that "natural" data won't have a mean and median that differ too greatly from one another, so this should also be acceptable. It is however not as well known as the mean, and so your users might not be expecting it, especially if you call it an "average".
answered Dec 5 '18 at 23:27
RandomMathGuyRandomMathGuy
641
$endgroup$
add a comment |
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3027809%2fwhich-average-would-make-the-most-sense-mean-mode-median%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
I'm not sure that there is a mathematical answer to this question, as each statistic has their use. But, for what it is worth, here is my opinion on each three:
1) Tried and true, the mean is what people think of when they hear the word "average". Not a lot can go wrong with this statistic unless someone adds a note so severely out of tune that it isn't even the right note anymore.
2) Mode is almost certainly useless for you unless you plan on "bucketing" your results into small cent intervals, and even then you would do better to provide the entire histogram rather than just the mode.
3) The median is an excellent way of providing midpoint data, and it will help suppress outliers. I think it is fair to say, in general, that "natural" data won't have a mean and median that differ too greatly from one another, so this should also be acceptable. It is however not as well known as the mean, and so your users might not be expecting it, especially if you call it an "average".
answered Dec 5 '18 at 23:27
RandomMathGuyRandomMathGuy
641
$endgroup$
add a comment |
$begingroup$
I'm not sure that there is a mathematical answer to this question, as each statistic has their use. But, for what it is worth, here is my opinion on each three:
1) Tried and true, the mean is what people think of when they hear the word "average". Not a lot can go wrong with this statistic unless someone adds a note so severely out of tune that it isn't even the right note anymore.
2) Mode is almost certainly useless for you unless you plan on "bucketing" your results into small cent intervals, and even then you would do better to provide the entire histogram rather than just the mode.
3) The median is an excellent way of providing midpoint data, and it will help suppress outliers. I think it is fair to say, in general, that "natural" data won't have a mean and median that differ too greatly from one another, so this should also be acceptable. It is however not as well known as the mean, and so your users might not be expecting it, especially if you call it an "average".
answered Dec 5 '18 at 23:27
RandomMathGuyRandomMathGuy
641
$endgroup$
add a comment |
$begingroup$
I'm not sure that there is a mathematical answer to this question, as each statistic has their use. But, for what it is worth, here is my opinion on each three:
1) Tried and true, the mean is what people think of when they hear the word "average". Not a lot can go wrong with this statistic unless someone adds a note so severely out of tune that it isn't even the right note anymore.
2) Mode is almost certainly useless for you unless you plan on "bucketing" your results into small cent intervals, and even then you would do better to provide the entire histogram rather than just the mode.
3) The median is an excellent way of providing midpoint data, and it will help suppress outliers. I think it is fair to say, in general, that "natural" data won't have a mean and median that differ too greatly from one another, so this should also be acceptable. It is however not as well known as the mean, and so your users might not be expecting it, especially if you call it an "average".
answered Dec 5 '18 at 23:27
RandomMathGuyRandomMathGuy
641
$endgroup$
I'm not sure that there is a mathematical answer to this question, as each statistic has their use. But, for what it is worth, here is my opinion on each three:
1) Tried and true, the mean is what people think of when they hear the word "average". Not a lot can go wrong with this statistic unless someone adds a note so severely out of tune that it isn't even the right note anymore.
2) Mode is almost certainly useless for you unless you plan on "bucketing" your results into small cent intervals, and even then you would do better to provide the entire histogram rather than just the mode.
3) The median is an excellent way of providing midpoint data, and it will help suppress outliers. I think it is fair to say, in general, that "natural" data won't have a mean and median that differ too greatly from one another, so this should also be acceptable. It is however not as well known as the mean, and so your users might not be expecting it, especially if you call it an "average".
answered Dec 5 '18 at 23:27
RandomMathGuyRandomMathGuy
641
answered Dec 5 '18 at 23:27
RandomMathGuyRandomMathGuy
641
answered Dec 5 '18 at 23:27
RandomMathGuyRandomMathGuy
641
answered Dec 5 '18 at 23:27
RandomMathGuyRandomMathGuy
641
641
add a comment |
add a comment |
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3027809%2fwhich-average-would-make-the-most-sense-mean-mode-median%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
$begingroup$
It depends on whether you want to indicate that they have bias (e.g. they generally tend to tune to too high a pitch, or generally too low) or dispersion (they are not very good at getting the correct pitch).
$endgroup$
– Henry
Dec 5 '18 at 23:27