Sketch two normal distributions whose means are equal but whose standard deviations are different. | Numerade (2024)

`); let searchUrl = `/search/`; history.forEach((elem) => { prevsearch.find('#prevsearch-options').append(`

${elem}

`); }); } $('#search-pretype-options').empty(); $('#search-pretype-options').append(prevsearch); let prevbooks = $(false); [ {title:"Recently Opened Textbooks", books:previous_books}, {title:"Recommended Textbooks", books:recommended_books} ].forEach((book_segment) => { if (Array.isArray(book_segment.books) && book_segment.books.length>0 && nsegments<2) { nsegments+=1; prevbooks = $(`

  • ${book_segment.title}
  • `); let searchUrl = "/books/xxx/"; book_segment.books.forEach((elem) => { prevbooks.find('#prevbooks-options'+nsegments.toString()).append(`

    ${elem.title} ${ordinal(elem.edition)} ${elem.author}

    `); }); } $('#search-pretype-options').append(prevbooks); }); } function anon_pretype() { let prebooks = null; try { prebooks = JSON.parse(localStorage.getItem('PRETYPE_BOOKS_ANON')); }catch(e) {} if ('previous_books' in prebooks && 'recommended_books' in prebooks) { previous_books = prebooks.previous_books; recommended_books = prebooks.recommended_books; if (typeof PREVBOOKS !== 'undefined' && Array.isArray(PREVBOOKS)) { new_prevbooks = PREVBOOKS; previous_books.forEach(elem => { for (let i = 0; i < new_prevbooks.length; i++) { if (elem.id == new_prevbooks[i].id) { return; } } new_prevbooks.push(elem); }); new_prevbooks = new_prevbooks.slice(0,3); previous_books = new_prevbooks; } if (typeof RECBOOKS !== 'undefined' && Array.isArray(RECBOOKS)) { new_recbooks = RECBOOKS; for (let j = 0; j < new_recbooks.length; j++) { new_recbooks[j].viewed_at = new Date(); } let insert = true; for (let i=0; i < recommended_books.length; i++){ for (let j = 0; j < new_recbooks.length; j++) { if (recommended_books[i].id == new_recbooks[j].id) { insert = false; } } if (insert){ new_recbooks.push(recommended_books[i]); } } new_recbooks.sort((a,b)=>{ adate = new Date(2000, 0, 1); bdate = new Date(2000, 0, 1); if ('viewed_at' in a) {adate = new Date(a.viewed_at);} if ('viewed_at' in b) {bdate = new Date(b.viewed_at);} // 100000000: instead of just erasing the suggestions from previous week, // we just move them to the back of the queue acurweek = ((new Date()).getDate()-adate.getDate()>7)?0:100000000; bcurweek = ((new Date()).getDate()-bdate.getDate()>7)?0:100000000; aviews = 0; bviews = 0; if ('views' in a) {aviews = acurweek+a.views;} if ('views' in b) {bviews = bcurweek+b.views;} return bviews - aviews; }); new_recbooks = new_recbooks.slice(0,3); recommended_books = new_recbooks; } localStorage.setItem('PRETYPE_BOOKS_ANON', JSON.stringify({ previous_books: previous_books, recommended_books: recommended_books })); build_popup(); } } var whiletyping_search_object = null; var whiletyping_search = { books: [], curriculum: [], topics: [] } var single_whiletyping_ajax_promise = null; var whiletyping_database_initial_burst = 0; //number of consecutive calls, after 3 we start the 1 per 5 min calls function get_whiletyping_database() { //gets the database from the server. // 1. by validating against a local database value we confirm that the framework is working and // reduce the ammount of continuous calls produced by errors to 1 per 5 minutes. return localforage.getItem('whiletyping_last_attempt').then(function(value) { if ( value==null || (new Date()) - (new Date(value)) > 1000*60*5 || (whiletyping_database_initial_burst < 3) ) { localforage.setItem('whiletyping_last_attempt', (new Date()).getTime()); // 2. Make an ajax call to the server and get the search database. let databaseUrl = `/search/whiletype_database/`; let resp = single_whiletyping_ajax_promise; if (resp === null) { whiletyping_database_initial_burst = whiletyping_database_initial_burst + 1; single_whiletyping_ajax_promise = resp = new Promise((resolve, reject) => { $.ajax({ url: databaseUrl, type: 'POST', data:{csrfmiddlewaretoken: "qQ6rCNig1nv3yZ730lxdDA8r6kJuxCyxspVpmWls7PDN3W920GddHM8OFKhaZkiZ"}, success: function (data) { // 3. verify that the elements of the database exist and are arrays if ( ('books' in data) && ('curriculum' in data) && ('topics' in data) && Array.isArray(data.books) && Array.isArray(data.curriculum) && Array.isArray(data.topics)) { localforage.setItem('whiletyping_last_success', (new Date()).getTime()); localforage.setItem('whiletyping_database', data); resolve(data); } }, error: function (error) { console.log(error); resolve(null); }, complete: function (data) { single_whiletyping_ajax_promise = null; } }) }); } return resp; } return Promise.resolve(null); }).catch(function(err) { console.log(err); return Promise.resolve(null); }); } function get_whiletyping_search_object() { // gets the fuse objects that will be in charge of the search if (whiletyping_search_object){ return Promise.resolve(whiletyping_search_object); } database_promise = localforage.getItem('whiletyping_database').then(function(database) { return localforage.getItem('whiletyping_last_success').then(function(last_success) { if (database==null || (new Date()) - (new Date(last_success)) > 1000*60*60*24*30 || (new Date('2023-04-25T00:00:00')) - (new Date(last_success)) > 0) { // New database update return get_whiletyping_database().then(function(new_database) { if (new_database) { database = new_database; } return database; }); } else { return Promise.resolve(database); } }); }); return database_promise.then(function(database) { if (database) { const options = { isCaseSensitive: false, includeScore: true, shouldSort: true, // includeMatches: false, // findAllMatches: false, // minMatchCharLength: 1, // location: 0, threshold: 0.2, // distance: 100, // useExtendedSearch: false, ignoreLocation: true, // ignoreFieldNorm: false, // fieldNormWeight: 1, keys: [ "title" ] }; let curriculum_index={}; let topics_index={}; database.curriculum.forEach(c => curriculum_index[c.id]=c); database.topics.forEach(t => topics_index[t.id]=t); for (j=0; j

    Solutions
  • Textbooks
  • `); } function build_solutions() { if (Array.isArray(solution_search_result)) { const viewAllHTML = userSubscribed ? `View All` : ''; var solutions_section = $(`
  • Solutions ${viewAllHTML}
  • `); let questionUrl = "/questions/xxx/"; let askUrl = "/ask/question/xxx/"; solution_search_result.forEach((elem) => { let url = ('course' in elem)?askUrl:questionUrl; let solution_type = ('course' in elem)?'ask':'question'; let subtitle = ('course' in elem)?(elem.course??""):(elem.book ?? "")+"    "+(elem.chapter?"Chapter "+elem.chapter:""); solutions_section.find('#whiletyping-solutions').append(` ${elem.text} ${subtitle} `); }); $('#search-solution-options').empty(); if (Array.isArray(solution_search_result) && solution_search_result.length>0){ $('#search-solution-options').append(solutions_section); } MathJax.typesetPromise([document.getElementById('search-solution-options')]); } } function build_textbooks() { $('#search-pretype-options').empty(); $('#search-pretype-options').append($('#search-solution-options').html()); if (Array.isArray(textbook_search_result)) { var books_section = $(`
  • Textbooks View All
  • `); let searchUrl = "/books/xxx/"; textbook_search_result.forEach((elem) => { books_section.find('#whiletyping-books').append(` ${elem.title} ${ordinal(elem.edition)} ${elem.author} `); }); } if (Array.isArray(textbook_search_result) && textbook_search_result.length>0){ $('#search-pretype-options').append(books_section); } } function build_popup(first_time = false) { if ($('#search-text').val()=='') { build_pretype(); } else { solution_and_textbook_search(); } } var search_text_out = true; var search_popup_out = true; const is_login = false; const user_hash = null; function pretype_setup() { $('#search-text').focusin(function() { $('#search-popup').addClass('show'); resize_popup(); search_text_out = false; }); $( window ).resize(function() { resize_popup(); }); $('#search-text').focusout(() => { search_text_out = true; if (search_text_out && search_popup_out) { $('#search-popup').removeClass('show'); } }); $('#search-popup').mouseenter(() => { search_popup_out = false; }); $('#search-popup').mouseleave(() => { search_popup_out = true; if (search_text_out && search_popup_out) { $('#search-popup').removeClass('show'); } }); $('#search-text').on("keyup", delay(() => { build_popup(); }, 200)); build_popup(true); let prevbookUrl = `/search/pretype_books/`; let prebooks = null; try { prebooks = JSON.parse(localStorage.getItem('PRETYPE_BOOKS_'+(is_login?user_hash:'ANON'))); }catch(e) {} if (prebooks && 'previous_books' in prebooks && 'recommended_books' in prebooks) { if (is_login) { previous_books = prebooks.previous_books; recommended_books = prebooks.recommended_books; if (prebooks.time && new Date().getTime()-prebooks.time<1000*60*60*6) { build_popup(); return; } } else { anon_pretype(); return; } } $.ajax({ url: prevbookUrl, method: 'POST', data:{csrfmiddlewaretoken: "qQ6rCNig1nv3yZ730lxdDA8r6kJuxCyxspVpmWls7PDN3W920GddHM8OFKhaZkiZ"}, success: function(response){ previous_books = response.previous_books; recommended_books = response.recommended_books; if (is_login) { localStorage.setItem('PRETYPE_BOOKS_'+user_hash, JSON.stringify({ previous_books: previous_books, recommended_books: recommended_books, time: new Date().getTime() })); } build_popup(); }, error: function(response){ console.log(response); } }); } $( document ).ready(pretype_setup); $( document ).ready(function(){ $('#search-popup').on('click', '.search-view-item', function(e) { e.preventDefault(); let autoCompleteSearchViewUrl = `/search/autocomplete_search_view/`; let objectUrl = $(this).attr('href'); let selectedId = $(this).data('objid'); let searchResults = []; $("#whiletyping-solutions").find("a").each(function() { let is_selected = selectedId === $(this).data('objid'); searchResults.push({ objectId: $(this).data('objid'), contentType: $(this).data('contenttype'), category: $(this).data('category'), selected: is_selected }); }); $("#whiletyping-books").find("a").each(function() { let is_selected = selectedId === $(this).data('objid'); searchResults.push({ objectId: $(this).data('objid'), contentType: $(this).data('contenttype'), category: $(this).data('category'), selected: is_selected }); }); $.ajax({ url: autoCompleteSearchViewUrl, method: 'POST', data:{ csrfmiddlewaretoken: "qQ6rCNig1nv3yZ730lxdDA8r6kJuxCyxspVpmWls7PDN3W920GddHM8OFKhaZkiZ", query: $('#search-text').val(), searchObjects: JSON.stringify(searchResults) }, dataType: 'json', complete: function(data){ window.location.href = objectUrl; } }); }); });
    Sketch two normal distributions whose means are equal but whose standard deviations are different. | Numerade (2024)

    FAQs

    Is it possible to have normal distributions with different means but the same standard deviations? ›

    In spite of the relationship between their means, two normal distributions with the same standard deviation will have the same spread. As shown in the below figure, the two variables have the same mean and same standard deviation but different distributions. So, the statement given is true.

    Do two normally distributed variables that have the same mean and standard deviation have the same distribution? ›

    Consider "two normally distributed variables with same mean and standard deviation have the same distribution. The mean and standard deviation determine the normally distributed. So, two normally distributed variables with same mean and standard deviation have the same shape. Hence, the given statement is true.

    When comparing two normal distributions with the same mean but different standard deviations, the one with the smaller standard deviation would? ›

    A larger standard deviation results in a flatter and more spread out curve, while a smaller standard deviation leads to a taller and narrower curve.

    Which distribution has the mean and standard deviation equal to each other? ›

    The standard normal distribution Z with mean value μ = 0 and standard deviation σ = 1. The standard normal distribution may be used to represent any normal distribution, provided you think in terms of the number of standard deviations above or below the mean. The standard normal probability table, shown in Table 7.3.

    Can two samples have the same mean but different standard deviations? ›

    If the sample mean of the two data sets is the same, it means that the two data sets are centrally located around the same value. Whereas for the standard deviation which measures the spread of the data from the central value and hence, it can be different.

    Is possible for two distributions to have the same range but different variances? ›

    Yes, two sets of data can have the same mean but not the same variance. It implies that the center value of the two sets is the same, but the spread or the dispersion of the data values around that center value is different.

    How do you know if two normal distributions are different? ›

    One way is to look at the mean and standard deviation. The mean should be close to zero and the standard deviation should be close to one. Another way to evaluate normal distribution is to look at the skewness and kurtosis. Skewness should be close to zero and kurtosis should be close to three.

    Can two sets of data have the same mean but not the same variance? ›

    Yes, two sets of data have the same mean, but not the same variance. Two data sets may have the same mean, but different variances. The data set with numbers at the extremes will have more variance than those with numbers near the mean.

    What is the standard deviation of the difference of two distributions? ›

    Answer: The expression for calculating the standard deviation of the difference between two means is given by z = [(x1 - x2) - (µ1 - µ2)] / sqrt ( σ12 / n1 + σ22 / n2)

    What is a normal distribution with mean and standard deviation called? ›

    Z scores (also known as standard scores): the number of standard deviations that a given raw score falls above or below the mean. Standard normal distribution: a normal distribution represented in z scores. The standard normal distribution always has a mean of zero and a standard deviation of one.

    How to find both mean and standard deviation in normal distribution? ›

    Answer. In order to find the unknown mean 𝜇 and standard deviation 𝜎 , we code 𝑋 by the change of variables 𝑋 ↦ 𝑍 = 𝑋 − 𝜇 𝜎 . Now 𝑍 ∼ 𝑁  0 , 1   follows the standard normal distribution and 𝑃 ( 𝑋 ≤ 7 2 . 4 4 ) = 𝑃  𝑍 ≤ 7 2 .

    Is deviation always positive? ›

    Whenever, there are two unequal terms in the observations, the standard deviation is positive, that means greater than zero. If all the observations are exactly equal, then the standard deviation is exactly zero.So, under no circ*mstances, the standard deviation can be negative or less than zero.

    Can two different normal distributions have different means and the same standard deviation? ›

    For some probability distributions a like the normal distribution the mean and the variance are independent and there fire can have equal means and different with the same standard deviation. They can have different means and the same standard deviations. However this is not true for most other distributions.

    What does it mean when the mean is equal to the standard deviation? ›

    If you have a normal variable with mean = standard deviation, then it has a 16% probability of being negative (i.e. Φ[−1]=0.16, see here). So a non-negative variable can only be truncated normal at best.

    What is the standard deviation if all the data values are equal to the mean? ›

    If all the data values are identical, the mean will be equal to all the data values. This means that no value will deviate away from the mean. This means that the standard deviation of the set will be zero as there is no deviation as all the values are situated at the mean.

    Can a normal distribution have any mean and standard deviation? ›

    Standard normal distribution: a normal distribution represented in z scores. The standard normal distribution always has a mean of zero and a standard deviation of one.

    Can normal distributions differ in their means? ›

    Normal distributions can differ in their means and in their standard deviations. Figure 1 shows three normal distributions.

    Do some normal probability distributions have equal arithmetic means but their standard deviations may be different? ›

    Yes, it is possible for normal distributions to have the same means, while also having different standard deviations. The mean of a normal distribution determines where the distribution is centered, while the standard deviation expresses something about the spread, variability, or dispersion of the distribution.

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