{"id":586,"date":"2024-06-19T08:23:32","date_gmt":"2024-06-19T05:23:32","guid":{"rendered":"https:\/\/sisu.ut.ee\/measurement\/self-test-3-4\/"},"modified":"2024-06-19T08:23:32","modified_gmt":"2024-06-19T05:23:32","slug":"self-test-3-4","status":"publish","type":"page","link":"https:\/\/sisu.ut.ee\/measurement\/self-test-3-4\/","title":{"rendered":"Self-test 3.4"},"content":{"rendered":"<div id=\"watupro_quiz\" class=\"quiz-area single-page-quiz\">\n<p id=\"submittingExam11\" style=\"display:none;text-align:center;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/sisu.ut.ee\/wp-content\/plugins\/watupro\/img\/loading.gif\" width=\"16\" height=\"16\"><\/p>\n\n<div class=\"watupro-exam-description\" id=\"description-quiz-11\"><p>Here you can test whether you have correctly understood the concept of standard deviation of the mean and its calculation.<\/p>\n<\/div>\n\n<form action=\"\" method=\"post\" class=\"quiz-form\" id=\"quiz-11\" enctype=\"multipart\/form-data\">\n<div class=\"watu-question \" id=\"question-1\" style=\";\"><div id=\"questionWrap-1\" class=\"   watupro-question-id-39\">\n\t\t\t<div class=\"question-content\"><div><span class=\"watupro_num\">1. <\/span>A number of parallel measurements of a quantity <em>X<\/em>\u00a0 are performed on identical samples under identical conditions and values <em>x<\/em><sub>1<\/sub>, <em>x<\/em><sub>2<\/sub>, .. <em>x<sub>n<\/sub><\/em> are obtained. Mark the correct statements.<\/div><input type=\"hidden\" name=\"question_id[]\" id=\"qID_1\" value=\"39\" class=\"watupro-question-id\"><input type=\"hidden\" id=\"answerType39\" class=\"answerTypeCnt1\" value=\"checkbox\"><!-- end question-content--><\/div><div class=\"question-choices watupro-choices-columns \" id=\"questionChoices39\"><div class=\"watupro-question-choice  \" dir=\"auto\"><input type=\"checkbox\" name=\"answer-39[]\" id=\"answer-id-148\" class=\"answer   answerof-39 \" value=\"148\"><label for=\"answer-id-148\" id=\"answer-label-148\" class=\" answer\"><span><p>Standard deviation of the mean can be calculated by dividing the experimental standard deviation by the square root of the number of measurements.\u00a0<\/p><\/span><\/label><\/div><div class=\"watupro-question-choice  \" dir=\"auto\"><input type=\"checkbox\" name=\"answer-39[]\" id=\"answer-id-149\" class=\"answer   answerof-39 \" value=\"149\"><label for=\"answer-id-149\" id=\"answer-label-149\" class=\" answer\"><span><p>Standard deviation of the mean can be used as the estimate of standard uncertainty (caused by the repeatability) of <em>X \u00a0<\/em>if the mean <em>x<\/em><sub>m<\/sub> is used as the value of <em>X\u00a0<\/em> in the model.<\/p><\/span><\/label><\/div><div class=\"watupro-question-choice  \" dir=\"auto\"><input type=\"checkbox\" name=\"answer-39[]\" id=\"answer-id-145\" class=\"answer   answerof-39 \" value=\"145\"><label for=\"answer-id-145\" id=\"answer-label-145\" class=\" answer\"><span><p>Standard deviation of the mean can be calculated by summing up all values and dividing the sum with the number of values.\u00a0<\/p><\/span><\/label><\/div><div class=\"watupro-question-choice  \" dir=\"auto\"><input type=\"checkbox\" name=\"answer-39[]\" id=\"answer-id-146\" class=\"answer   answerof-39 \" value=\"146\"><label for=\"answer-id-146\" id=\"answer-label-146\" class=\" answer\"><span><p>The standard deviation of the mean can be calculated according to equation <img loading=\"lazy\" decoding=\"async\" width=\"129\" height=\"18\" class=\"alignnone wp-image-311\" style=\"vertical-align: middle;\" src=\"https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/18\/3-4-1.png\" title=\"3-4-1.png\" alt=\"3-4-1.png\"><em><br><\/em><\/p><\/span><\/label><\/div><div class=\"watupro-question-choice  \" dir=\"auto\"><input type=\"checkbox\" name=\"answer-39[]\" id=\"answer-id-147\" class=\"answer   answerof-39 \" value=\"147\"><label for=\"answer-id-147\" id=\"answer-label-147\" class=\" answer\"><span><p>Standard deviation of the mean can be calculated by dividing the experimental standard deviation by square root of three.<\/p><\/span><\/label><\/div><div class=\"watupro-question-choice  \" dir=\"auto\"><input type=\"checkbox\" name=\"answer-39[]\" id=\"answer-id-150\" class=\"answer   answerof-39 \" value=\"150\"><label for=\"answer-id-150\" id=\"answer-label-150\" class=\" answer\"><span><p>Standard deviation of the mean is often denoted as <em>s<\/em>(<em>x<\/em><sub>m<\/sub>).\u00a0<\/p><\/span><\/label><\/div><!-- end question-choices--><\/div><!-- end questionWrap--><\/div>\t\t\t\t\t<div style=\"display:none;\" id=\"liveResult-1\">\t\t   \n\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/sisu.ut.ee\/wp-content\/plugins\/watupro\/img\/loading.gif\" width=\"16\" height=\"16\" alt=\"Loading...\" title=\"Loading...\">\u00a0Loading...\t\t\t\t\t<\/div>\t\n\t\t\t<\/div> \n\t   \t<p id=\"liveResBtn-39\" style=\"clear:both;\"><input type=\"button\" id=\"liveResultBtn39\" class=\"liveResultBtn1 watupro-live-result-btn\" value=\"See Answer\" onclick=\"WatuPRO.liveResult(39, 1);\"><\/p>\n\t   <div class=\"watu-question \" id=\"question-2\" style=\";\"><div id=\"questionWrap-2\" class=\"   watupro-question-id-40\">\n\t\t\t<div class=\"question-content\"><span class=\"watupro_num\">2. <\/span>Equation <img loading=\"lazy\" decoding=\"async\" width=\"254\" height=\"70\" class=\"alignnone wp-image-317\" style=\"vertical-align: middle;\" title=\"3-3-2-valem.png\" src=\"https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/18\/3-3-2-valem.png\" alt=\"3-3-2-valem.png\">\u00a0\u00a0is given. What are the symbols used in this equation?<div class=\"question-choices\"><table class=\"question-choices watupro-matrix-droppable\" id=\"watuPROMatrixDroppable_40\"><tr><td class=\"watupro-matrix-left-cell\">1. <em>s<\/em>(<em>x<\/em><sub>m<\/sub>)<\/td>\n\t\t\t\t\t\t<td class=\"watupro-matrix-right-cell watuPRODroppable40\" id=\"watuPRODroppableCell151\"><div class=\"question-choices\"><div class=\"watupro-matrix-right\"><div id=\"watuproNMatrixSelection-0-0\" class=\" watupro-matrix-draggable watupro-nmatrix-answer-0\" onclick=\"WatuPROINMatrix.sel(this, 'watuPRODroppableCell151', 0);return false;\">arithmetic mean<!--WTPMD5d0bdd60bd02e5e1f7aeb579fea87e626--><p class=\"watupro-nmatrix-unselect\">Unselect<\/p><\/div><div id=\"watuproNMatrixSelection-0-1\" class=\" watupro-matrix-draggable watupro-nmatrix-answer-1\" onclick=\"WatuPROINMatrix.sel(this, 'watuPRODroppableCell151', 1);return false;\">number of measurements<!--WTPMD5f19d798524454b6a9f18c66a231216c3--><p class=\"watupro-nmatrix-unselect\">Unselect<\/p><\/div><div id=\"watuproNMatrixSelection-0-2\" class=\" watupro-matrix-draggable watupro-nmatrix-answer-2\" onclick=\"WatuPROINMatrix.sel(this, 'watuPRODroppableCell151', 2);return false;\">standard deviation<!--WTPMD570122e6380205ddb985968a5c75d5d66--><p class=\"watupro-nmatrix-unselect\">Unselect<\/p><\/div><div id=\"watuproNMatrixSelection-0-3\" class=\" watupro-matrix-draggable watupro-nmatrix-answer-3\" onclick=\"WatuPROINMatrix.sel(this, 'watuPRODroppableCell151', 3);return false;\">standard deviation of the mean<!--WTPMD55464c04bc5f49fe99de1a0bf91be537c--><p class=\"watupro-nmatrix-unselect\">Unselect<\/p><\/div><div id=\"watuproNMatrixSelection-0-4\" class=\" watupro-matrix-draggable watupro-nmatrix-answer-4\" onclick=\"WatuPROINMatrix.sel(this, 'watuPRODroppableCell151', 4);return false;\">i-th individual result<!--WTPMD5bfeb3a8f934963e18f736ceca58af1d0--><p class=\"watupro-nmatrix-unselect\">Unselect<\/p><\/div><\/div><\/div><input type=\"hidden\" class=\"answerof-40 watupro-nmatrix-answer-field\" id=\"field-watuPRODroppableCell151\" name=\"matrix-left-151\" value=\"\"><\/td><\/tr><tr><td class=\"watupro-matrix-left-cell\">2. <em>s<\/em>(<em>x<\/em>)<\/td>\n\t\t\t\t\t\t<td class=\"watupro-matrix-right-cell watuPRODroppable40\" id=\"watuPRODroppableCell152\"><div class=\"question-choices\"><div class=\"watupro-matrix-right\"><div id=\"watuproNMatrixSelection-1-0\" class=\" watupro-matrix-draggable watupro-nmatrix-answer-0\" onclick=\"WatuPROINMatrix.sel(this, 'watuPRODroppableCell152', 0);return false;\">arithmetic mean<!--WTPMD5d0bdd60bd02e5e1f7aeb579fea87e626--><p class=\"watupro-nmatrix-unselect\">Unselect<\/p><\/div><div id=\"watuproNMatrixSelection-1-1\" class=\" watupro-matrix-draggable watupro-nmatrix-answer-1\" onclick=\"WatuPROINMatrix.sel(this, 'watuPRODroppableCell152', 1);return false;\">number of measurements<!--WTPMD5f19d798524454b6a9f18c66a231216c3--><p class=\"watupro-nmatrix-unselect\">Unselect<\/p><\/div><div id=\"watuproNMatrixSelection-1-2\" class=\" watupro-matrix-draggable watupro-nmatrix-answer-2\" onclick=\"WatuPROINMatrix.sel(this, 'watuPRODroppableCell152', 2);return false;\">standard deviation<!--WTPMD570122e6380205ddb985968a5c75d5d66--><p class=\"watupro-nmatrix-unselect\">Unselect<\/p><\/div><div id=\"watuproNMatrixSelection-1-3\" class=\" watupro-matrix-draggable watupro-nmatrix-answer-3\" onclick=\"WatuPROINMatrix.sel(this, 'watuPRODroppableCell152', 3);return false;\">standard deviation of the mean<!--WTPMD55464c04bc5f49fe99de1a0bf91be537c--><p class=\"watupro-nmatrix-unselect\">Unselect<\/p><\/div><div id=\"watuproNMatrixSelection-1-4\" class=\" watupro-matrix-draggable watupro-nmatrix-answer-4\" onclick=\"WatuPROINMatrix.sel(this, 'watuPRODroppableCell152', 4);return false;\">i-th individual result<!--WTPMD5bfeb3a8f934963e18f736ceca58af1d0--><p class=\"watupro-nmatrix-unselect\">Unselect<\/p><\/div><\/div><\/div><input type=\"hidden\" class=\"answerof-40 watupro-nmatrix-answer-field\" id=\"field-watuPRODroppableCell152\" name=\"matrix-left-152\" value=\"\"><\/td><\/tr><tr><td class=\"watupro-matrix-left-cell\">3. <em>x<\/em><sub>m<\/sub><\/td>\n\t\t\t\t\t\t<td class=\"watupro-matrix-right-cell watuPRODroppable40\" id=\"watuPRODroppableCell153\"><div class=\"question-choices\"><div class=\"watupro-matrix-right\"><div id=\"watuproNMatrixSelection-2-0\" class=\" watupro-matrix-draggable watupro-nmatrix-answer-0\" onclick=\"WatuPROINMatrix.sel(this, 'watuPRODroppableCell153', 0);return false;\">arithmetic mean<!--WTPMD5d0bdd60bd02e5e1f7aeb579fea87e626--><p class=\"watupro-nmatrix-unselect\">Unselect<\/p><\/div><div id=\"watuproNMatrixSelection-2-1\" class=\" watupro-matrix-draggable watupro-nmatrix-answer-1\" onclick=\"WatuPROINMatrix.sel(this, 'watuPRODroppableCell153', 1);return false;\">number of measurements<!--WTPMD5f19d798524454b6a9f18c66a231216c3--><p class=\"watupro-nmatrix-unselect\">Unselect<\/p><\/div><div id=\"watuproNMatrixSelection-2-2\" class=\" watupro-matrix-draggable watupro-nmatrix-answer-2\" onclick=\"WatuPROINMatrix.sel(this, 'watuPRODroppableCell153', 2);return false;\">standard deviation<!--WTPMD570122e6380205ddb985968a5c75d5d66--><p class=\"watupro-nmatrix-unselect\">Unselect<\/p><\/div><div id=\"watuproNMatrixSelection-2-3\" class=\" watupro-matrix-draggable watupro-nmatrix-answer-3\" onclick=\"WatuPROINMatrix.sel(this, 'watuPRODroppableCell153', 3);return false;\">standard deviation of the mean<!--WTPMD55464c04bc5f49fe99de1a0bf91be537c--><p class=\"watupro-nmatrix-unselect\">Unselect<\/p><\/div><div id=\"watuproNMatrixSelection-2-4\" class=\" watupro-matrix-draggable watupro-nmatrix-answer-4\" onclick=\"WatuPROINMatrix.sel(this, 'watuPRODroppableCell153', 4);return false;\">i-th individual result<!--WTPMD5bfeb3a8f934963e18f736ceca58af1d0--><p class=\"watupro-nmatrix-unselect\">Unselect<\/p><\/div><\/div><\/div><input type=\"hidden\" class=\"answerof-40 watupro-nmatrix-answer-field\" id=\"field-watuPRODroppableCell153\" name=\"matrix-left-153\" value=\"\"><\/td><\/tr><tr><td class=\"watupro-matrix-left-cell\">4. <em>x<\/em><sub>i<\/sub><\/td>\n\t\t\t\t\t\t<td class=\"watupro-matrix-right-cell watuPRODroppable40\" id=\"watuPRODroppableCell154\"><div class=\"question-choices\"><div class=\"watupro-matrix-right\"><div id=\"watuproNMatrixSelection-3-0\" class=\" watupro-matrix-draggable watupro-nmatrix-answer-0\" onclick=\"WatuPROINMatrix.sel(this, 'watuPRODroppableCell154', 0);return false;\">arithmetic mean<!--WTPMD5d0bdd60bd02e5e1f7aeb579fea87e626--><p class=\"watupro-nmatrix-unselect\">Unselect<\/p><\/div><div id=\"watuproNMatrixSelection-3-1\" class=\" watupro-matrix-draggable watupro-nmatrix-answer-1\" onclick=\"WatuPROINMatrix.sel(this, 'watuPRODroppableCell154', 1);return false;\">number of measurements<!--WTPMD5f19d798524454b6a9f18c66a231216c3--><p class=\"watupro-nmatrix-unselect\">Unselect<\/p><\/div><div id=\"watuproNMatrixSelection-3-2\" class=\" watupro-matrix-draggable watupro-nmatrix-answer-2\" onclick=\"WatuPROINMatrix.sel(this, 'watuPRODroppableCell154', 2);return false;\">standard deviation<!--WTPMD570122e6380205ddb985968a5c75d5d66--><p class=\"watupro-nmatrix-unselect\">Unselect<\/p><\/div><div id=\"watuproNMatrixSelection-3-3\" class=\" watupro-matrix-draggable watupro-nmatrix-answer-3\" onclick=\"WatuPROINMatrix.sel(this, 'watuPRODroppableCell154', 3);return false;\">standard deviation of the mean<!--WTPMD55464c04bc5f49fe99de1a0bf91be537c--><p class=\"watupro-nmatrix-unselect\">Unselect<\/p><\/div><div id=\"watuproNMatrixSelection-3-4\" class=\" watupro-matrix-draggable watupro-nmatrix-answer-4\" onclick=\"WatuPROINMatrix.sel(this, 'watuPRODroppableCell154', 4);return false;\">i-th individual result<!--WTPMD5bfeb3a8f934963e18f736ceca58af1d0--><p class=\"watupro-nmatrix-unselect\">Unselect<\/p><\/div><\/div><\/div><input type=\"hidden\" class=\"answerof-40 watupro-nmatrix-answer-field\" id=\"field-watuPRODroppableCell154\" name=\"matrix-left-154\" value=\"\"><\/td><\/tr><tr><td class=\"watupro-matrix-left-cell\">5. <em>n<\/em><\/td>\n\t\t\t\t\t\t<td class=\"watupro-matrix-right-cell watuPRODroppable40\" id=\"watuPRODroppableCell155\"><div class=\"question-choices\"><div class=\"watupro-matrix-right\"><div id=\"watuproNMatrixSelection-4-0\" class=\" watupro-matrix-draggable watupro-nmatrix-answer-0\" onclick=\"WatuPROINMatrix.sel(this, 'watuPRODroppableCell155', 0);return false;\">arithmetic mean<!--WTPMD5d0bdd60bd02e5e1f7aeb579fea87e626--><p class=\"watupro-nmatrix-unselect\">Unselect<\/p><\/div><div id=\"watuproNMatrixSelection-4-1\" class=\" watupro-matrix-draggable watupro-nmatrix-answer-1\" onclick=\"WatuPROINMatrix.sel(this, 'watuPRODroppableCell155', 1);return false;\">number of measurements<!--WTPMD5f19d798524454b6a9f18c66a231216c3--><p class=\"watupro-nmatrix-unselect\">Unselect<\/p><\/div><div id=\"watuproNMatrixSelection-4-2\" class=\" watupro-matrix-draggable watupro-nmatrix-answer-2\" onclick=\"WatuPROINMatrix.sel(this, 'watuPRODroppableCell155', 2);return false;\">standard deviation<!--WTPMD570122e6380205ddb985968a5c75d5d66--><p class=\"watupro-nmatrix-unselect\">Unselect<\/p><\/div><div id=\"watuproNMatrixSelection-4-3\" class=\" watupro-matrix-draggable watupro-nmatrix-answer-3\" onclick=\"WatuPROINMatrix.sel(this, 'watuPRODroppableCell155', 3);return false;\">standard deviation of the mean<!--WTPMD55464c04bc5f49fe99de1a0bf91be537c--><p class=\"watupro-nmatrix-unselect\">Unselect<\/p><\/div><div id=\"watuproNMatrixSelection-4-4\" class=\" watupro-matrix-draggable watupro-nmatrix-answer-4\" onclick=\"WatuPROINMatrix.sel(this, 'watuPRODroppableCell155', 4);return false;\">i-th individual result<!--WTPMD5bfeb3a8f934963e18f736ceca58af1d0--><p class=\"watupro-nmatrix-unselect\">Unselect<\/p><\/div><\/div><\/div><input type=\"hidden\" class=\"answerof-40 watupro-nmatrix-answer-field\" id=\"field-watuPRODroppableCell155\" name=\"matrix-left-155\" value=\"\"><\/td><\/tr><\/table><\/div><input type=\"hidden\" name=\"question_id[]\" id=\"qID_2\" value=\"40\" class=\"watupro-question-id\"><input type=\"hidden\" id=\"answerType40\" class=\"answerTypeCnt2\" value=\"nmatrix\"><!-- end question-content--><\/div><!-- end questionWrap--><\/div>\t\t\t\t\t<div style=\"display:none;\" id=\"liveResult-2\">\t\t   \n\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/sisu.ut.ee\/wp-content\/plugins\/watupro\/img\/loading.gif\" width=\"16\" height=\"16\" alt=\"Loading...\" title=\"Loading...\">\u00a0Loading...\t\t\t\t\t<\/div>\t\n\t\t\t<\/div> \n\t   \t<p id=\"liveResBtn-40\" style=\"clear:both;\"><input type=\"button\" id=\"liveResultBtn40\" class=\"liveResultBtn2 watupro-live-result-btn\" value=\"See Answer\" onclick=\"WatuPRO.liveResult(40, 2);\"><\/p>\n\t   <div style=\"display:none\" id=\"question-3\">\n\t<div class=\"question-content\">\n\t\t<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/sisu.ut.ee\/wp-content\/plugins\/watupro\/img\/loading.gif\" width=\"16\" height=\"16\" alt=\"Loading...\" title=\"Loading...\">\u00a0Loading...\t<\/div>\n<\/div>\n\n<br>\n\t\n\t\t\t<div class=\"watupro_buttons flex \" id=\"watuPROButtons11\">\n\t\t  <div id=\"prev-question\" style=\"display:none;\"><input type=\"button\" value=\"&lt; Previous\" onclick=\"WatuPRO.nextQuestion(event, 'previous');\"><\/div>\t\t  \t\t  \t\t   \n\t\t   \t  \t\t<div><input type=\"button\" name=\"action\" class=\"watupro-submit-button\" onclick=\"WatuPRO.submitResult(event)\" id=\"action-button\" value=\"View Results\">\n\t\t<\/div>\n\t\t<\/div>\n\t\t\n\t<input type=\"hidden\" name=\"quiz_id\" value=\"11\" id=\"watuPROExamID\">\n\t<input type=\"hidden\" name=\"start_time\" id=\"startTime\" value=\"2026-04-19 23:28:54\">\n\t<input type=\"hidden\" name=\"start_timestamp\" id=\"startTimeStamp\" value=\"1776641334\">\n\t<input type=\"hidden\" name=\"question_ids\" value=\"\">\n\t<input type=\"hidden\" name=\"watupro_questions\" value=\"39:148,149,145,146,147,150 | 40:151,152,153,154,155\">\n\t<input type=\"hidden\" name=\"no_ajax\" value=\"0\">\t\t\t<\/form>\n\t<p>\u00a0<\/p>\n<\/div>\n\n<script type=\"text\/javascript\">\n\/\/jQuery(document).ready(function(){\ndocument.addEventListener(\"DOMContentLoaded\", function(event) { \t\nvar question_ids = \"39,40\";\nWatuPROSettings[11] = {};\nWatuPRO.qArr = question_ids.split(',');\nWatuPRO.exam_id = 11;\t    \nWatuPRO.post_id = 586;\nWatuPRO.store_progress = 0;\nWatuPRO.curCatPage = 1;\nWatuPRO.requiredIDs=\"0\".split(\",\");\nWatuPRO.hAppID = \"0.93534100 1776630534\";\nvar url = \"https:\/\/sisu.ut.ee\/wp-content\/plugins\/watupro\/show_exam.php\";\nWatuPRO.examMode = 1;\nWatuPRO.siteURL=\"https:\/\/sisu.ut.ee\/measurement\/wp-admin\/admin-ajax.php\";\nWatuPRO.emailIsNotRequired = 0;\nWatuPRO.perDecade = 10;\nWatuPROIntel.init(11);\nWatuPRO.inCategoryPages=1;});    \t 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