{"id":54,"date":"2020-01-02T13:19:13","date_gmt":"2020-01-02T12:19:13","guid":{"rendered":"http:\/\/estatistika.ku.sk\/?page_id=54"},"modified":"2022-03-07T14:14:47","modified_gmt":"2022-03-07T13:14:47","slug":"54-2","status":"publish","type":"page","link":"https:\/\/estatistika.ku.sk\/index.php\/deskriptivna-statistika\/54-2\/","title":{"rendered":"\u0160tatistick\u00e9 ukazovatele"},"content":{"rendered":"<p style=\"text-align: justify;\"><span style=\"font-family: helvetica, arial, sans-serif; font-size: 14pt;\"><strong>\u0160tatistick\u00e9 ukazovatele MIERY POLOHY (resp. centr\u00e1lnej tendencie):<\/strong><\/span><\/p>\n<ul style=\"text-align: justify;\">\n<li><span style=\"font-family: helvetica, arial, sans-serif; font-size: 14pt;\"><span style=\"color: #ff0000;\"><strong>Aritmetick\u00fd priemer<\/strong> <\/span>(<em>Mean<\/em>) je mierou centr\u00e1lnej tendencie, s\u00fa to s\u010d\u00edtan\u00e9 v\u0161etky \u010d\u00edsla, ktor\u00e9 s\u00fa vydelen\u00e9 ich po\u010dtom. Priemer m\u00f4\u017eu v\u00fdrazne ovplyvni\u0165 extr\u00e9mne hodnoty. <strong>Pou\u017e\u00edvame len u kardin\u00e1lnych premenn\u00fdch.<\/strong><\/span><\/li>\n<li><span style=\"font-family: helvetica, arial, sans-serif; font-size: 14pt;\"><span style=\"color: #339966;\"><strong>Medi\u00e1n<\/strong> <\/span>(<em>Median<\/em>) \u2013 prostredn\u00e1 hodnota premennej. Plat\u00ed, \u017ee u d\u00e1t, ktor\u00e9 s\u00fa usporiadan\u00e9 pod\u013ea ve\u013ekosti je 50 % hodn\u00f4t men\u0161\u00edch alebo rovn\u00fdch a najmenej 50 % hodn\u00f4t je v\u00e4\u010d\u0161\u00edch, alebo rovn\u00fdch medi\u00e1nu. Ve\u013ekou v\u00fdhodou medi\u00e1nu je, \u017ee ho na rozdiel od priemeru neovplyv\u0148uj\u00fa extr\u00e9mne hodnoty. <strong>Pou\u017e\u00edva sa ako miera polohy u ordin\u00e1lnych premenn\u00fdch i pri kardin\u00e1lnych premenn\u00fdch. <\/strong>Nev\u00fdhodou naopak je, \u017ee na jeho ur\u010denie sa nepou\u017e\u00edvaj\u00fa re\u00e1lne hodnoty, ale len ich poradie.<\/span><\/li>\n<li><span style=\"font-family: helvetica, arial, sans-serif; font-size: 14pt;\"><span style=\"color: #3366ff;\"><strong>Modus<\/strong> <\/span>(<em>Mode<\/em>) \u2013 vyjadruje naj\u010dastej\u0161ie sa vyskytuj\u00facu hodnotu premennej. <strong>Je to jedin\u00e1 pr\u00edpustn\u00e1 \u0161tatistick\u00e1 miera pre nomin\u00e1lnu premenn\u00fa<\/strong>, m\u00f4\u017ee sa v\u0161ak po\u010d\u00edta\u0165 <strong>i z ordin\u00e1lnej a kardin\u00e1lnej premennej.\u00a0<\/strong><\/span><\/li>\n<\/ul>\n<p style=\"text-align: justify;\"><span style=\"font-family: helvetica, arial, sans-serif; font-size: 14pt;\">Na obr\u00e1zku je n\u00e1zorn\u00e1 uk\u00e1\u017eka vy\u0161\u0161ie spom\u00ednan\u00fdch \u0161tatistick\u00fdch ukazovate\u013eov miery polohy vo v\u00fdskumnom s\u00fabore. Uk\u00e1\u017eka sa t\u00fdka platu respondentov, pri\u010dom vid\u00edme, \u017ee <span style=\"color: #ff0000;\">priemern\u00fd plat<\/span> je 730 \u20ac, ale <span style=\"color: #008000;\">medi\u00e1n<\/span> je 500 \u20ac &#8211; to znamen\u00e1, \u017ee sa vo v\u00fdskumnom s\u00fabore vyskytuj\u00fa extr\u00e9mne hodnoty (vi\u010f respondenta, ktor\u00fd zar\u00e1ba 3000 \u20ac). <span style=\"color: #3366ff;\">Modus<\/span> je 300 \u20ac, t\u00e1to suma sa vo v\u00fdskumnom s\u00fabore vyskytuje naj\u010dastej\u0161ie (3 \u013eudia).<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: helvetica, arial, sans-serif; font-size: 14pt;\"><img fetchpriority=\"high\" decoding=\"async\" class=\"alignnone size-full wp-image-56\" src=\"http:\/\/estatistika.ku.sk\/wp-content\/uploads\/2020\/01\/panaky.jpg\" alt=\"\" width=\"1207\" height=\"437\" srcset=\"https:\/\/estatistika.ku.sk\/wp-content\/uploads\/2020\/01\/panaky.jpg 1207w, https:\/\/estatistika.ku.sk\/wp-content\/uploads\/2020\/01\/panaky-300x109.jpg 300w, https:\/\/estatistika.ku.sk\/wp-content\/uploads\/2020\/01\/panaky-1024x371.jpg 1024w, https:\/\/estatistika.ku.sk\/wp-content\/uploads\/2020\/01\/panaky-768x278.jpg 768w, https:\/\/estatistika.ku.sk\/wp-content\/uploads\/2020\/01\/panaky-1200x434.jpg 1200w\" sizes=\"(max-width: 1207px) 100vw, 1207px\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: helvetica, arial, sans-serif; font-size: 14pt;\">V tabu\u013eke s\u00fa preh\u013eadne uveden\u00e9 pr\u00edpustn\u00e9 \u0161tatistick\u00e9 ukazovatele miery polohy pre nomin\u00e1lnu, ordin\u00e1lnu a kardin\u00e1lnu premenn\u00fa.<!--[endif]--><img decoding=\"async\" class=\"alignnone size-full wp-image-58\" src=\"http:\/\/estatistika.ku.sk\/wp-content\/uploads\/2020\/01\/Sn\u00edmka.jpg\" alt=\"\" width=\"545\" height=\"114\" srcset=\"https:\/\/estatistika.ku.sk\/wp-content\/uploads\/2020\/01\/Sn\u00edmka.jpg 545w, https:\/\/estatistika.ku.sk\/wp-content\/uploads\/2020\/01\/Sn\u00edmka-300x63.jpg 300w\" sizes=\"(max-width: 545px) 100vw, 545px\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: helvetica, arial, sans-serif; font-size: 14pt;\"><strong>Interval spo\u013eahlivosti pre <span style=\"color: #ff0000;\">priemer<\/span><\/strong><\/span><br \/>\n<span style=\"font-family: helvetica, arial, sans-serif; font-size: 14pt;\">\u010eal\u0161\u00edm v\u00fdznamn\u00fdm deskript\u00edvnym ukazovate\u013eom je tzv. interval spo\u013eahlivosti pre priemer. Tento interval n\u00e1m poskytne inform\u00e1ciu, v akom rozsahu hodn\u00f4t by sa mohla nach\u00e1dza\u0165 skuto\u010dn\u00e1 priemern\u00e1 hodnota premennej v celej popul\u00e1cii (z\u00e1kladnom s\u00fabore).<\/span><\/p>\n<p><span style=\"font-family: helvetica, arial, sans-serif; font-size: 14pt;\"><strong>V\u00fdpo\u010det intervalu spo\u013eahlivosti v SPSS<\/strong>: <strong>Cesta<\/strong><em>: \u2013 Analyze\u00a0 Descriptive Statistics &#8211; Explore<\/em><\/span><\/p>\n<p><span style=\"font-family: helvetica, arial, sans-serif; font-size: 14pt;\"><strong>V\u00fdpo\u010det intervalu spo\u013eahlivosti v Exceli<\/strong>: vi\u010f <a href=\"http:\/\/estatistika.ku.sk\/index.php\/induktivna-statistika\/komparacna-analyza\/komparacia-suborov-podla-kardinalnej-premennej-2\/elementor-393\/\">videon\u00e1vod<\/a><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: helvetica, arial, sans-serif; font-size: 14pt;\">\u0160tatistick\u00e9 ukazovatele <strong>MIERY VARIABILITY (resp. miery rozptylu):<\/strong><\/span><\/p>\n<ul style=\"text-align: justify;\">\n<li><span style=\"font-family: helvetica, arial, sans-serif; font-size: 14pt;\"><strong>Rozp\u00e4tie<\/strong> (<em>Range<\/em>) \u2013 vyjadruje rozdiel medzi najv\u00e4\u010d\u0161ou a najmen\u0161ou nameranou hodnotou sk\u00famanej premennej (max \u2013 min). Ide o najjednoduch\u0161iu mieru variability.<\/span><\/li>\n<li><span style=\"font-family: helvetica, arial, sans-serif; font-size: 14pt;\"><strong>Medzikvartilov\u00e9 rozp\u00e4tie<\/strong> (<em>Interquartile range<\/em>) &#8211; predstavuje rozdiel medzi tret\u00edm a prv\u00fdm kvartilom (75. a 25. percentilom), \u010do reprezentuje oblas\u0165 stredn\u00fdch 50 % hodn\u00f4t premennej.<\/span><\/li>\n<li><span style=\"font-family: helvetica, arial, sans-serif; font-size: 14pt;\"><strong>\u0160tandardn\u00e1 odch\u00fdlka<\/strong> (<em>Std. deviation<\/em>) \u2013 informuje o tom, ak\u00fd je rozdiel medzi hodnotou a priemernou hodnotou sledovanej premennej. Ak je hodnota \u0161tandardnej odch\u00fdlky vysok\u00e1, znamen\u00e1 to, \u017ee v\u0161etky \u010d\u00edsla v ur\u010ditom s\u00fabore sa medzi sebou zna\u010dne l\u00ed\u0161ia. Ak je hodnota \u0161tandardnej odch\u00fdlky n\u00edzka, znamen\u00e1 to, \u017ee v\u0161etky \u010d\u00edsla s\u00fa koncentrovan\u00e9 okolo priemernej hodnoty.<\/span><\/li>\n<\/ul>\n<blockquote><p><span style=\"font-family: helvetica, arial, sans-serif; font-size: 14pt;\">Pre podrobnej\u0161ie inform\u00e1cie o \u0161tandardnej odch\u00fdlke <a href=\"http:\/\/estatistika.ku.sk\/index.php\/standardna-odchylka\/\">klikni sem<\/a>.<\/span><\/p><\/blockquote>\n<p style=\"text-align: justify;\"><span style=\"font-family: helvetica, arial, sans-serif; font-size: 14pt;\">\u0160tatistick\u00e9 ukazovatele <strong>MIERY TVARU (resp. miery distrib\u00facie):<\/strong><\/span><\/p>\n<ul style=\"text-align: justify;\">\n<li><span style=\"font-family: helvetica, arial, sans-serif; font-size: 14pt;\"><strong>\u0160ikmos\u0165<\/strong> (<em>Skewness<\/em>) \u2013 meria smer a stupe\u0148 asymetrie rozdelenia premennej (Rimar\u010d\u00edk, 2007). Koeficient je kladn\u00fd v pr\u00edpade, \u017ee priemer je v\u00e4\u010d\u0161\u00ed ako medi\u00e1n, teda v\u00e4\u010d\u0161ina hodn\u00f4t je men\u0161ia ako priemer (kladn\u00e1 \u0161ikmos\u0165). Koeficient je z\u00e1porn\u00fd v pr\u00edpade, \u017ee medi\u00e1n je v\u00e4\u010d\u0161\u00ed ako priemer a teda v\u00e4\u010d\u0161ina hodn\u00f4t je v\u00e4\u010d\u0161ia ako priemer (z\u00e1porn\u00e1 \u0161ikmos\u0165). <strong>Koeficient rovn\u00fd 0 znamen\u00e1 symetrick\u00e9\u00a0(norm\u00e1lne) rozdelenie.<\/strong><img decoding=\"async\" class=\"wp-image-205 aligncenter\" src=\"http:\/\/estatistika.ku.sk\/wp-content\/uploads\/2020\/01\/Sn\u00edmka123.jpg\" alt=\"\" width=\"492\" height=\"377\" srcset=\"https:\/\/estatistika.ku.sk\/wp-content\/uploads\/2020\/01\/Sn\u00edmka123.jpg 587w, https:\/\/estatistika.ku.sk\/wp-content\/uploads\/2020\/01\/Sn\u00edmka123-300x230.jpg 300w\" sizes=\"(max-width: 492px) 100vw, 492px\" \/><\/span><\/li>\n<\/ul>\n<ul style=\"text-align: justify;\">\n<li><span style=\"font-family: helvetica, arial, sans-serif; font-size: 14pt;\"><strong>Strmos\u0165\/\u0161picatos\u0165<\/strong> (<em>Kurtosis<\/em>) \u2013 charakterizuje v\u00fdskyt extr\u00e9mne vysok\u00fdch a extr\u00e9mne n\u00edzkych hodn\u00f4t. \u0160picatos\u0165 rozdelenia sa porovn\u00e1va so \u0161picatos\u0165ou norm\u00e1lneho rozdelenia, ktor\u00e9 m\u00e1 hodnotu 0. Ak je \u0161picatos\u0165 vy\u0161\u0161ia, hodnoty s\u00fa s\u00fastreden\u00e9 okolo stredu, naopak \u010d\u00edm je rozdelenie menej \u0161picat\u00e9, teda plochej\u0161ie, hodnoty s\u00fa od tohto stredu vzdialenej\u0161ie.<\/span><\/li>\n<\/ul>\n<p style=\"text-align: justify;\"><span style=\"font-family: helvetica, arial, sans-serif; font-size: 14pt;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-211\" src=\"http:\/\/estatistika.ku.sk\/wp-content\/uploads\/2020\/01\/Sn\u00edmka9.jpg\" alt=\"\" width=\"374\" height=\"180\" srcset=\"https:\/\/estatistika.ku.sk\/wp-content\/uploads\/2020\/01\/Sn\u00edmka9.jpg 374w, https:\/\/estatistika.ku.sk\/wp-content\/uploads\/2020\/01\/Sn\u00edmka9-300x144.jpg 300w\" sizes=\"(max-width: 374px) 100vw, 374px\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: helvetica, arial, sans-serif; font-size: 14pt;\">V\u00fdpo\u010det \u0161tatistick\u00fdch ukazovate\u013eov v programe Excel n\u00e1jdete vo videon\u00e1vode ni\u017e\u0161ie, videon\u00e1vod v programe SPSS, ak kliknete <a href=\"http:\/\/estatistika.ku.sk\/index.php\/deskriptivna-statistika\/druhostupnove-triedenie-dat\/\">sem<\/a>.<\/span><\/p>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 100%; text-align: center;\"><strong><span style=\"font-family: helvetica, arial, sans-serif;\">Videon\u00e1vod: SPSS<\/span><\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 100%;\"><iframe title=\"Testovanie zhody priemeru s kon\u0161tantou\" width=\"580\" height=\"326\" src=\"https:\/\/www.youtube.com\/embed\/V2RbSAXIHcs?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n","protected":false},"excerpt":{"rendered":"<p>\u0160tatistick\u00e9 ukazovatele MIERY POLOHY (resp. centr\u00e1lnej tendencie): Aritmetick\u00fd priemer (Mean) je mierou centr\u00e1lnej tendencie, s\u00fa to s\u010d\u00edtan\u00e9 v\u0161etky \u010d\u00edsla, ktor\u00e9 s\u00fa vydelen\u00e9 ich po\u010dtom. Priemer m\u00f4\u017eu v\u00fdrazne ovplyvni\u0165 extr\u00e9mne hodnoty. Pou\u017e\u00edvame len u kardin\u00e1lnych premenn\u00fdch. Medi\u00e1n (Median) \u2013 prostredn\u00e1 hodnota premennej. Plat\u00ed, \u017ee u d\u00e1t, ktor\u00e9 s\u00fa usporiadan\u00e9 pod\u013ea ve\u013ekosti je 50 % hodn\u00f4t men\u0161\u00edch [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"parent":13,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"templates\/template-full-width.php","meta":{"footnotes":""},"class_list":["post-54","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/estatistika.ku.sk\/index.php\/wp-json\/wp\/v2\/pages\/54","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/estatistika.ku.sk\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/estatistika.ku.sk\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/estatistika.ku.sk\/index.php\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/estatistika.ku.sk\/index.php\/wp-json\/wp\/v2\/comments?post=54"}],"version-history":[{"count":30,"href":"https:\/\/estatistika.ku.sk\/index.php\/wp-json\/wp\/v2\/pages\/54\/revisions"}],"predecessor-version":[{"id":2273,"href":"https:\/\/estatistika.ku.sk\/index.php\/wp-json\/wp\/v2\/pages\/54\/revisions\/2273"}],"up":[{"embeddable":true,"href":"https:\/\/estatistika.ku.sk\/index.php\/wp-json\/wp\/v2\/pages\/13"}],"wp:attachment":[{"href":"https:\/\/estatistika.ku.sk\/index.php\/wp-json\/wp\/v2\/media?parent=54"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}