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Sınıf Matematik Dersi: Veri Analizi ve Merkezi Eğilim Ölçüleri","beginTime":0}],"fullResult":[{"index":0,"title":"Altıncı Sınıf Matematik Çalışması","list":{"type":"unordered","items":["Altıncı sınıf matematik kitabının sayfa 92 ile 101 arasındaki çalışmaları birlikte yapılacak.","\"Harçlıklarım ve Harcamalarım\" başlıklı etkinlik dört'te kalmış.","Ercan Bey'in Anka ve Dua adında iki kızı vardır ve her birine günlük 100 TL harçlık vermektedir."]},"beginTime":2,"endTime":47,"href":"/video/preview/1996425864624660898?parent-reqid=1769502989319675-5024056911704190247-balancer-l7leveler-kubr-yp-vla-34-BAL&text=MathiXD94&t=2&ask_summarization=1"},{"index":1,"title":"Harcama Verileri ve Merkezi Eğilim Ölçüleri","list":{"type":"unordered","items":["Anka ve Dua'nın bir hafta boyunca yaptığı harcamalar ve ücretler tabloda yer almaktadır.","Öğrenciler beş-altı kişilik gruplara ayrılarak tablolara göre soruları cevaplayacaklardır.","İlk soruda Anka ve Dua'nın harcadığı günlük para miktarlarının aritmetik ortalaması ayrı ayrı bulunması istenmektedir."]},"beginTime":47,"endTime":105,"href":"/video/preview/1996425864624660898?parent-reqid=1769502989319675-5024056911704190247-balancer-l7leveler-kubr-yp-vla-34-BAL&text=MathiXD94&t=47&ask_summarization=1"},{"index":2,"title":"Anka'nın Harcama Verileri","list":{"type":"unordered","items":["Anka'nın pazartesi günü su ve simit (15 TL), salı günü ayran ve simit (20 TL), süt ve çikolata (30 TL), perşembe günü sandviç (40 TL), cuma günü kuruyemiş (50 TL), cumartesi günü kalem (55 TL) almıştır.","Anka'nın harcadığı günlük para miktarları yakın bir dağılım sergilemiştir.","Aritmetik ortalama merkezi eğilim ölçüsü Anka için daha mantıklıdır."]},"beginTime":105,"endTime":155,"href":"/video/preview/1996425864624660898?parent-reqid=1769502989319675-5024056911704190247-balancer-l7leveler-kubr-yp-vla-34-BAL&text=MathiXD94&t=105&ask_summarization=1"},{"index":3,"title":"Dua'nın Harcama Verileri","list":{"type":"unordered","items":["Dua'nın pazartesi günü su (5 TL), salı günü ayran ve simit (20 TL), çarşamba günü meyveli yoğurt (30 TL), perşembe günü su (5 TL), cuma günü ayran (10 TL), cumartesi günü müze bileti (70 TL), pazar günü tiyatro bileti (70 TL) almıştır.","Dua'nın harcadığı günlük para miktarları arasında açık bir fark vardır.","Ortanca merkezi eğilim ölçüsü Dua için daha mantıklıdır."]},"beginTime":155,"endTime":219,"href":"/video/preview/1996425864624660898?parent-reqid=1769502989319675-5024056911704190247-balancer-l7leveler-kubr-yp-vla-34-BAL&text=MathiXD94&t=155&ask_summarization=1"},{"index":4,"title":"Aritmetik Ortalama Hesaplamaları","list":{"type":"unordered","items":["Anka'nın harcadığı günlük para miktarlarının aritmetik ortalaması 30 TL olarak bulunmuştur.","Dua'nın harcadığı günlük para miktarlarının aritmetik ortalaması da 30 TL olarak bulunmuştur.","Her iki durumda da aritmetik ortalama 30 TL olarak çıkmış olsa da, Anka için aritmetik ortalama, Dua için ortanca merkezi eğilim ölçüsü tercih edilmelidir."]},"beginTime":219,"endTime":382,"href":"/video/preview/1996425864624660898?parent-reqid=1769502989319675-5024056911704190247-balancer-l7leveler-kubr-yp-vla-34-BAL&text=MathiXD94&t=219&ask_summarization=1"},{"index":5,"title":"Biriktirme Verileri ve Merkezi Eğilim Ölçüleri","list":{"type":"unordered","items":["Anka'nın biriktirdiği günlük para miktarlarının aritmetik ortalaması 70 TL olarak bulunmuştur.","Dua'nın biriktirdiği günlük para miktarlarının aritmetik ortalaması da 70 TL olarak bulunmuştur.","Her iki durumda da biriktirme verileri arasında açık bir fark olduğundan, ortanca merkezi eğilim ölçüsü tercih edilmelidir."]},"beginTime":382,"endTime":521,"href":"/video/preview/1996425864624660898?parent-reqid=1769502989319675-5024056911704190247-balancer-l7leveler-kubr-yp-vla-34-BAL&text=MathiXD94&t=382&ask_summarization=1"},{"index":6,"title":"Diğer Örnekler","list":{"type":"unordered","items":["Altıncı sınıfındaki kız ve erkek öğrencilerin matematik dersinden aldığı notlar incelenmiştir.","Kız öğrenciler için açıklık fazla olduğu için ortanca merkezi eğilim ölçüsü tercih edilmelidir.","Erkek öğrenciler için tekrar eden sayılar olduğu için tepe değeri merkezi eğilim ölçüsü tercih edilmelidir."]},"beginTime":521,"endTime":652,"href":"/video/preview/1996425864624660898?parent-reqid=1769502989319675-5024056911704190247-balancer-l7leveler-kubr-yp-vla-34-BAL&text=MathiXD94&t=521&ask_summarization=1"},{"index":7,"title":"Bilinçli Harcama Etkinliği","list":{"type":"unordered","items":["Etkinlik beş \"Bilinçli Harcama\" kapsamında sınıf arkadaşlarının kitap alma alışkanlıklarını öğrenmek için bir anket yapılacaktır.","Sınıftan bir kişi seçerek tüm öğrencilere \"Yılda kaç kez kitap satın alıyorsunuz?\" sorusu sorulacaktır.","Elde edilen veriler kullanılarak aritmetik ortalama, ortanca ve tepe değeri merkezi eğilim ölçüleri hesaplanacaktır."]},"beginTime":652,"endTime":684,"href":"/video/preview/1996425864624660898?parent-reqid=1769502989319675-5024056911704190247-balancer-l7leveler-kubr-yp-vla-34-BAL&text=MathiXD94&t=652&ask_summarization=1"},{"index":8,"title":"Veri Görselleştirme ve Kök Yaprak Tablosu","list":{"type":"unordered","items":["Sınıfta kitap alma sıklığı verileri (yılda kaç kez kitap satın alındığı) küçükten büyüğe doğru sıralanarak görselleştirme aracı seçilerek özetlenmelidir.","Kök yaprak tablosu, diğer tablolara göre daha küçük ve verileri daha kolay açıklayan bir görselleştirme aracıdır.","Kök yaprak tablosu, verileri daha kısa şekilde özetleyerek zaman ve yer tasarrufu sağlar."]},"beginTime":686,"endTime":909,"href":"/video/preview/1996425864624660898?parent-reqid=1769502989319675-5024056911704190247-balancer-l7leveler-kubr-yp-vla-34-BAL&text=MathiXD94&t=686&ask_summarization=1"},{"index":9,"title":"Merkezi Eğilim Ölçüleri","list":{"type":"unordered","items":["Aritmetik ortalama, tüm verilerin toplamının veri sayısına bölünmesiyle hesaplanır ve yaklaşık ne kadar kitap alım satım olduğunu ifade eder.","Ortanca, verilerin tam ortasındaki terimlerin toplamının yarısına eşittir ve yaklaşık kitap alım sayısını ifade eder.","Tepe değer, en çok tekrar eden değerdir ve yaklaşık kaç kitap alım yapıldığını ifade eder."]},"beginTime":909,"endTime":1211,"href":"/video/preview/1996425864624660898?parent-reqid=1769502989319675-5024056911704190247-balancer-l7leveler-kubr-yp-vla-34-BAL&text=MathiXD94&t=909&ask_summarization=1"},{"index":10,"title":"Merkezi Eğilim Ölçüleri Arasındaki Farklar","list":{"type":"unordered","items":["Aritmetik ortalama ve tepe değer arasında fark vardır ve bu fark verilerin dağılımından kaynaklanır.","Sınıftaki herkesin aynı sayıda kitabı aldığı durumda merkezi eğilim ölçüleri arasında farklılıklar olmaz.","Merkezi eğilim ölçülerinin veriler hakkında her zaman doğru bilgi vermediği, yaklaşık değerler verdiği ve bazı durumlarda hata veya sapmalar olabileceği belirtilmiştir."]},"beginTime":1211,"endTime":1398,"href":"/video/preview/1996425864624660898?parent-reqid=1769502989319675-5024056911704190247-balancer-l7leveler-kubr-yp-vla-34-BAL&text=MathiXD94&t=1211&ask_summarization=1"},{"index":11,"title":"Bilinçli Harcama","list":{"type":"unordered","items":["Bilinçli harcama yapmayı isteyen biri kitap ihtiyacını kütüphanelerden karşılayabilir.","Kütüphaneleri kullanarak kitap alım sayısını azaltmak mümkündür."]},"beginTime":1398,"endTime":1494,"href":"/video/preview/1996425864624660898?parent-reqid=1769502989319675-5024056911704190247-balancer-l7leveler-kubr-yp-vla-34-BAL&text=MathiXD94&t=1398&ask_summarization=1"},{"index":12,"title":"Finansal Okuryazarlık Kavramı","list":{"type":"unordered","items":["Aybüke ve babası bir bilim kültür dergisinde finansal okuryazarlık kavramına dikkat çekti ve bu konuda daha fazla bilgi edinmeye karar verdiler.","Finansal okuryazarlık, insanların finansal kararlar alırken gerekli bilgilere sahip olma, bu bilgileri anlama ve değerlendirme yeteneği olarak tanımlanabilir.","Finansal okuryazarlık, bireylerin gelecekteki ihtiyaçlarını düşünerek mevcut paralarını ve kaynaklarını nasıl yöneteceklerini bilmesi de bu kavramın önemli bir parçasıdır."]},"beginTime":1497,"endTime":1545,"href":"/video/preview/1996425864624660898?parent-reqid=1769502989319675-5024056911704190247-balancer-l7leveler-kubr-yp-vla-34-BAL&text=MathiXD94&t=1497&ask_summarization=1"},{"index":13,"title":"Bilgisayar Fiyatı Analizi","list":{"type":"unordered","items":["Aybüke'nin babası, bilgisayar almak isteyen kızına bir görev verdi: yıl içinde almak istediği bilgisayarın fiyatını takip et ve en uygun satın alma zamanını belirle.","Aybüke, bilgisayarın fiyatını etkileyen değişimleri izlemek için çeşitli genel ağ sitelerini araştırdı ve farklı zamanlarda bilgisayarın fiyatları ile ilgili verileri topladı.","Aybüke, fiyatların hangi dönemlerde düştüğünü ve yükseldiğini kaydederek bu bilgileri analiz etmeye başladı."]},"beginTime":1545,"endTime":1594,"href":"/video/preview/1996425864624660898?parent-reqid=1769502989319675-5024056911704190247-balancer-l7leveler-kubr-yp-vla-34-BAL&text=MathiXD94&t=1545&ask_summarization=1"},{"index":14,"title":"Matematiksel Analiz Soruları","list":{"type":"unordered","items":["İlk on ay içinde bilgisayarın ortalama fiyatı 12.410 TL olarak hesaplandı.","İlk on ay içinde bilgisayarın en sık tekrar eden fiyatları 12.200 TL, 12.500 TL ve 12.600 TL olarak bulundu.","İlk on ay için bilgisayarın fiyatı küçükten büyüğe sıralandığında ortadaki değer 12.450 TL olarak hesaplandı."]},"beginTime":1594,"endTime":1936,"href":"/video/preview/1996425864624660898?parent-reqid=1769502989319675-5024056911704190247-balancer-l7leveler-kubr-yp-vla-34-BAL&text=MathiXD94&t=1594&ask_summarization=1"},{"index":15,"title":"Açıklık ve En Uygun Satın Alma Zamanı","list":{"type":"unordered","items":["İlk on ay içinde bilgisayarın en düşük değeri 12.100 TL, en yüksek değeri 12.700 TL olarak bulundu ve açıklık 600 TL olarak hesaplandı.","Bilgisayarın ilk on ay içinde alınacak en uygun zamanı Ekim ayı olarak belirlendi çünkü bu ayda fiyat 12.100 TL'ye düşmüştü.","Ekim ayındaki fiyat, merkezi eğilim ölçülerinden herhangi birinin değeriyle örtüşmüyordu."]},"beginTime":1936,"endTime":2137,"href":"/video/preview/1996425864624660898?parent-reqid=1769502989319675-5024056911704190247-balancer-l7leveler-kubr-yp-vla-34-BAL&text=MathiXD94&t=1936&ask_summarization=1"},{"index":16,"title":"Spor Dalı Analizi","list":{"type":"unordered","items":["Bir ortaokulda \"En çok hangi spor dalını seviyorsunuz?\" sorusu sorulmuş ve kız ve erkek öğrencilerden alınan cevaplara göre iki ayrı sıklık tablosu oluşturulmuştur.","Tek bir tabloya bakarak ortaokulda en çok sevilen spor dalı ile ilgili yorum yapılamaz çünkü kızlar voleybol, erkekler ise futbolu en çok seçmiştir.","Güvenilir ve doğru yorum yapabilmek için verilen tablolardan yararlanarak \"Öğrencilerin en çok sevdiği spor dalları\" şeklinde bir tablo oluşturulması önerilmiştir."]},"beginTime":2137,"endTime":2282,"href":"/video/preview/1996425864624660898?parent-reqid=1769502989319675-5024056911704190247-balancer-l7leveler-kubr-yp-vla-34-BAL&text=MathiXD94&t=2137&ask_summarization=1"},{"index":17,"title":"Spor Dalları Tablosu Oluşturma","list":{"type":"unordered","items":["Spor dalı şeklinde bir tablo oluşturuldu ve spor dalları ile cinsiyet (kız ve erkek) ikili bir tablo oluşturuldu.","Tabloda futbol, voleybol, basketbol, buz pateni, hentbol ve okçuluk gibi spor dalları yer aldı.","Kız ve erkek öğrencilerin spor dallarına göre sayıları tabloya farklı kalemlerle dolduruldu."]},"beginTime":2301,"endTime":2449,"href":"/video/preview/1996425864624660898?parent-reqid=1769502989319675-5024056911704190247-balancer-l7leveler-kubr-yp-vla-34-BAL&text=MathiXD94&t=2301&ask_summarization=1"},{"index":18,"title":"Spor Dalları Analizi","list":{"type":"unordered","items":["Oluşturulan tabloya göre ortaokulda en çok sevilen spor dalları voleybol ve basketbol olup, her ikisi de 32 öğrenci tarafından tercih edildi.","En az sevilen spor dalı hentbol olup, sadece 12 öğrenci tarafından tercih edildi.","Tek tablo, verileri daha kolay inceleme ve analiz etme olanağı sağladı."]},"beginTime":2449,"endTime":2572,"href":"/video/preview/1996425864624660898?parent-reqid=1769502989319675-5024056911704190247-balancer-l7leveler-kubr-yp-vla-34-BAL&text=MathiXD94&t=2449&ask_summarization=1"},{"index":19,"title":"Kişisel Verilerin Gizliliği","list":{"type":"unordered","items":["Kişisel veriler, ad, yaş, telefon numarası, fotoğraflar, okul bilgileri ve sevilen oyunlar gibi kişisel bilgileri içerir.","Kişisel veriler ele geçirildiğinde özel reklamlar gösterilebilir veya kötü amaçlarla kullanılabilir.","Kişisel Verileri Koruma Kurumu, kişisel verilerin korunmasını sağlamak ve farkındalık oluşturmak için hizmet vermektedir."]},"beginTime":2572,"endTime":2723,"href":"/video/preview/1996425864624660898?parent-reqid=1769502989319675-5024056911704190247-balancer-l7leveler-kubr-yp-vla-34-BAL&text=MathiXD94&t=2572&ask_summarization=1"},{"index":20,"title":"Kişisel Verilerin Korunması İçin Dikkat Edilmesi Gerekenler","list":{"type":"unordered","items":["Kişisel veriler üçüncü kişilerle paylaşılmamalıdır.","Aydınlatma hükümlerini iyi incelemek ve izin işlemlerinde dikkatli olmak gerekir.","Yurt dışındaki kişilerle iletişimde dikkatli olunmalı, aksi takdirde veriler yurtdışına kaçırılabilir."]},"beginTime":2723,"endTime":2857,"href":"/video/preview/1996425864624660898?parent-reqid=1769502989319675-5024056911704190247-balancer-l7leveler-kubr-yp-vla-34-BAL&text=MathiXD94&t=2723&ask_summarization=1"},{"index":21,"title":"Erişebilirlik","list":{"type":"unordered","items":["Erişebilirlik, engelli ve engelsiz bireylerin bir ortam veya hizmeti kolayca bağımsız bir şekilde ulaşabilmesi ve kullanabilmesi anlamına gelir.","Fiziksel erişilebilirlik, bireylerin bina, açık alan ve toplu taşıma araçları gibi ortamlara engelsiz bir şekilde ulaşabilmesini kapsar.","Aile ve Sosyal Hizmetler Bakanlığı, erişilebilirlik belgesi vererek toplumda duyarlılık oluşturmaktadır."]},"beginTime":2857,"endTime":2925,"href":"/video/preview/1996425864624660898?parent-reqid=1769502989319675-5024056911704190247-balancer-l7leveler-kubr-yp-vla-34-BAL&text=MathiXD94&t=2857&ask_summarization=1"},{"index":22,"title":"Erişebilirlik Belgesi Verileri","list":{"type":"unordered","items":["Erişebilirlik belgesi alan yerlerin sayısı yıllara göre artmıştır, ancak 2021 yılında en zirve noktasına ulaşmıştır.","Erişebilirlik belgesi en fazla toplu taşıma araçlarında verilmiştir (1782 adet).","Engelli bireyler için biniş kolaylığı sağlanmayan durumlarda, topluma duyarlı bir vatandaş olarak bu durumu düzeltmek gerekir."]},"beginTime":2925,"endTime":3186,"href":"/video/preview/1996425864624660898?parent-reqid=1769502989319675-5024056911704190247-balancer-l7leveler-kubr-yp-vla-34-BAL&text=MathiXD94&t=2925&ask_summarization=1"}],"linkTemplate":"/video/preview/1996425864624660898?parent-reqid=1769502989319675-5024056911704190247-balancer-l7leveler-kubr-yp-vla-34-BAL&text=MathiXD94&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"6.sınıf matematik ders kitabı sayfa 92-93-94-95-96-97-98-99-100-101 // 6.sınıf matematik 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Öğretmen, ondalık sayılarla yapılan işlemler konusunu anlatmaktadır.","Videoda ondalık sayılarla toplama, çıkarma, çarpma ve bölme işlemlerinin adım adım çözümü gösterilmektedir. Öğretmen, virgülün konumunu belirleyerek işlemleri nasıl yapacağını, basamakları eşitleyerek çıkarma yapacağını ve çarpma işlemlerinde virgülün nasıl yerleştirileceğini detaylı şekilde açıklamaktadır. Video, konu testi beş kapsamında çeşitli matematik problemlerinin çözümünü içermektedir.","Videoda toplam 27 sorunun çözümü gösterilmekte olup, her bir işlemin nasıl yapılacağı adım adım anlatılmaktadır. Ayrıca ondalık sayıların rasyonel sayılarla çarpılması, bölünmesi ve toplanması gibi işlemler de detaylı olarak ele alınmaktadır."]},"endTime":1212,"title":"Matematik Dersi: Ondalık Sayılarla İşlemler","beginTime":0}],"fullResult":[{"index":0,"title":"Ondalık Sayılarla Çıkarma İşlemi","list":{"type":"unordered","items":["0,7'den 0,23'ü çıkarmak için virgüller alt alta getirildi ve basamaklar eşitlendi.","Çıkarma işlemi sonucunda 0,47 cevabı elde edildi."]},"beginTime":7,"endTime":37,"href":"/video/preview/11054677875862838252?parent-reqid=1769502989319675-5024056911704190247-balancer-l7leveler-kubr-yp-vla-34-BAL&text=MathiXD94&t=7&ask_summarization=1"},{"index":1,"title":"Ondalık Sayılarla Çarpma İşlemi","list":{"type":"unordered","items":["0,4 ile 0,1'i çarpmak için virgüller sağa dayalı yazıldı ve çarpma işlemi yapıldı.","Çarpma sonucunda virgülden sonra toplam üç basamak olduğu için sonuç 0,04 olarak 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Sınıf Matematik MEB Ders Kitabı Sayfa 94 Alıştırma Çözümleri 10. Sınıf Matematik MEB Ders Kitabı Sayfa 94 Alıştırma Çözümleri 10. Sınıf Matematik MEB Ders Kitabı Sayfa 94 Alıştırma Çözümleri...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/2408238/6ee4d0164a3fd872f4fa915fcf1b1492/564x318_1","videoSrc":"https://video-preview.s3.yandex.net/du297AAAAAA.mp4","videoType":"video/mp4"},"target":"_self","position":"7","reqid":"1769502989319675-5024056911704190247-balancer-l7leveler-kubr-yp-vla-34-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1769502989319675-5024056911704190247-balancer-l7leveler-kubr-yp-vla-34-BAL&text=videoid:7317520690247356339","teaser":[{"list":{"type":"unordered","items":["Bu video, bir matematik öğretmeni tarafından sunulan 10. sınıf Milli Eğitim matematik ders kitabının 94. sayfasındaki fonksiyonlar konusundaki alıştırmaların çözümlerini içeren eğitim içeriğidir.","Videoda öğretmen, fonksiyonlar konusunu ele alarak toplam on üç soruyu adım adım çözmektedir. Sorular arasında fonksiyon olup olmadığını inceleme, fonksiyon kuralını bulma, görüntü kümesini hesaplama, tanım kümesini bulma, fonksiyon değerlerini hesaplama, birebir, örten veya içine fonksiyonların belirlenmesi ve fonksiyonların cinsinden yazılması gibi konular yer almaktadır.","Her soru için detaylı açıklamalar yapılarak, fonksiyonların tanım ve görüntü kümelerinin nasıl belirleneceği, fonksiyon kurallarının nasıl uygulanacağı ve fonksiyonların birebir veya örten olması için gerekli koşullar gösterilmektedir."]},"endTime":1309,"title":"10. Sınıf Matematik Ders Kitabı Fonksiyonlar Konusu Çözümleri","beginTime":0}],"fullResult":[{"index":0,"title":"Matematik Ders Kitabı Alıştırmaları","list":{"type":"unordered","items":["10. sınıf Milli Eğitim matematik ders kitabının 94. sayfa alıştırmalarının çözümleri sunuluyor.","Öğrenciler takıldıkları soruları bu videodan izleyerek öğrenebilirler."]},"beginTime":3,"endTime":22,"href":"/video/preview/7317520690247356339?parent-reqid=1769502989319675-5024056911704190247-balancer-l7leveler-kubr-yp-vla-34-BAL&text=MathiXD94&t=3&ask_summarization=1"},{"index":1,"title":"Fonksiyonların Tanımlı Olup Olmadığı İncelenmesi","list":{"type":"unordered","items":["Fonksiyonlar tanım kümesindeki her eleman için görüntü kümesinde tek bir değer vermelidir.","Reel sayılar kümesinden reel sayılar kümesine tanımlı ifadeler genellikle fonksiyondur.","Kesirli ifadelerde paydaya dikkat edilmeli, payda sıfır olamaz, aksi takdirde fonksiyon değildir.","Tam sayılar kümesinden tam sayılar kümesine tanımlı ifadelerde, sonuç kesir çıkarsa fonksiyon değildir."]},"beginTime":22,"endTime":163,"href":"/video/preview/7317520690247356339?parent-reqid=1769502989319675-5024056911704190247-balancer-l7leveler-kubr-yp-vla-34-BAL&text=MathiXD94&t=22&ask_summarization=1"},{"index":2,"title":"Görüntü Kümesinin Bulunması","list":{"type":"unordered","items":["Fonksiyonun görüntü kümesi, tanım kümesindeki her eleman için fonksiyon kuralını uygulayarak bulunur.","Örneğin, f(x) = 5x + 4 fonksiyonunda, tanım kümesindeki her eleman için f(x) değeri hesaplanarak görüntü kümesi oluşturulur."]},"beginTime":163,"endTime":256,"href":"/video/preview/7317520690247356339?parent-reqid=1769502989319675-5024056911704190247-balancer-l7leveler-kubr-yp-vla-34-BAL&text=MathiXD94&t=163&ask_summarization=1"},{"index":3,"title":"Fonksiyon Denkleminin Kurulması","list":{"type":"unordered","items":["Fonksiyonun kuralı, verilen bilgilere göre kurulabilir.","Örneğin, \"her gerçek sayısının kendisinin karesinin beş eksiği\" ifadesi f(x) = x² - 5 fonksiyonunu verir.","Fonksiyonun belirli değerlerinin görüntüsü, fonksiyon kuralına yerleştirilerek bulunabilir."]},"beginTime":256,"endTime":344,"href":"/video/preview/7317520690247356339?parent-reqid=1769502989319675-5024056911704190247-balancer-l7leveler-kubr-yp-vla-34-BAL&text=MathiXD94&t=256&ask_summarization=1"},{"index":4,"title":"Tanım Kümesinin Bulunması","list":{"type":"unordered","items":["Görüntü kümesi verilmişse, tanım kümesi bulmak için fonksiyon kuralı görüntü değerleriyle eşitlenir.","Örneğin, f(x) = 2x - 9 fonksiyonunda, görüntü kümesi {5, 7, 11, 19} ise, her görüntü değeri için x değeri bulunarak tanım kümesi elde edilir."]},"beginTime":344,"endTime":425,"href":"/video/preview/7317520690247356339?parent-reqid=1769502989319675-5024056911704190247-balancer-l7leveler-kubr-yp-vla-34-BAL&text=MathiXD94&t=344&ask_summarization=1"},{"index":5,"title":"Fonksiyon Değerlerinin Hesaplanması","list":{"type":"unordered","items":["f(x+2) = 3x+4 fonksiyonunda, f(5) değeri için x+2 = 5 eşitliği çözülerek x = 3 bulunur.","f(x+5) değeri için x yerine x+3 yazılır ve fonksiyon kuralı uygulanır.","f(2x+1) değeri için x yerine 2x-1 yazılır ve fonksiyon kuralı uygulanır."]},"beginTime":425,"endTime":571,"href":"/video/preview/7317520690247356339?parent-reqid=1769502989319675-5024056911704190247-balancer-l7leveler-kubr-yp-vla-34-BAL&text=MathiXD94&t=425&ask_summarization=1"},{"index":6,"title":"Fonksiyon Denkleminin Çözülmesi","list":{"type":"unordered","items":["f(a+1) = 19 denklemi için, f(x+1) = 3(x+1) + 7 fonksiyon kuralı kullanılır.","Denklem çözülerek a = 3 bulunur."]},"beginTime":571,"endTime":615,"href":"/video/preview/7317520690247356339?parent-reqid=1769502989319675-5024056911704190247-balancer-l7leveler-kubr-yp-vla-34-BAL&text=MathiXD94&t=571&ask_summarization=1"},{"index":7,"title":"Birebir Fonksiyonlar","list":{"type":"unordered","items":["Birebir fonksiyon için her elemanın görüntüsü bir tane olmalı, bir elemanın iki elemana gidiyorsa birebir olmaz.","A şıkkındaki fonksiyon birebirdir.","B şıkkındaki fonksiyon birebir değildir çünkü f(0) = f(-1) = 0, iki eleman aynı değere gidiyor."]},"beginTime":617,"endTime":710,"href":"/video/preview/7317520690247356339?parent-reqid=1769502989319675-5024056911704190247-balancer-l7leveler-kubr-yp-vla-34-BAL&text=MathiXD94&t=617&ask_summarization=1"},{"index":8,"title":"Birebir Fonksiyonlar (Devam)","list":{"type":"unordered","items":["C şıkkındaki fonksiyon birebir değildir çünkü f(0) = f(1) = 0, iki eleman aynı değere gidiyor.","D şıkkındaki fonksiyon birebirdir çünkü pozitif reel sayılardan reel sayılara tanımlı ve her değeri için farklı bir sayı elde edilir."]},"beginTime":710,"endTime":792,"href":"/video/preview/7317520690247356339?parent-reqid=1769502989319675-5024056911704190247-balancer-l7leveler-kubr-yp-vla-34-BAL&text=MathiXD94&t=710&ask_summarization=1"},{"index":9,"title":"Örten ve İçine Fonksiyonlar","list":{"type":"unordered","items":["Örten fonksiyon, tanım kümesindeki her elemanın değer kümesindeki her elemana karşılık geldiği fonksiyondur.","A şıkkındaki fonksiyon örten fonksiyondur.","B şıkkındaki fonksiyon içine fonksiyondur çünkü sürekli pozitif sayılar elde edilir ve negatif sayıların karşılığı bulunamaz."]},"beginTime":792,"endTime":873,"href":"/video/preview/7317520690247356339?parent-reqid=1769502989319675-5024056911704190247-balancer-l7leveler-kubr-yp-vla-34-BAL&text=MathiXD94&t=792&ask_summarization=1"},{"index":10,"title":"İçine Fonksiyonlar (Devam)","list":{"type":"unordered","items":["C şıkkındaki fonksiyon içine fonksiyondur çünkü doğal sayılardan tam sayılara tanımlı ve tam sayılar içindeki bazı sayıların görüntüsü bulunamaz.","D şıkkındaki fonksiyon içine fonksiyondur çünkü sınırlı bir aralıktan tüm reel sayılara karşılık gelmez."]},"beginTime":873,"endTime":976,"href":"/video/preview/7317520690247356339?parent-reqid=1769502989319675-5024056911704190247-balancer-l7leveler-kubr-yp-vla-34-BAL&text=MathiXD94&t=873&ask_summarization=1"},{"index":11,"title":"Fonksiyon Değerleri","list":{"type":"unordered","items":["f(x+1) - 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Öğretmen, ders kitabından soruları çözerken öğrencilere adım adım rehberlik etmektedir.","Video, istatistikte merkezi eğilim ölçüleri (aritmetik ortalama, ortanca ve tepe değeri) ve veri yorumlama konularını ele almaktadır. İçerik üç ana bölümden oluşmaktadır: Türkiye'nin nüfus değişimini analiz etme, öğrencilerin kitap okuma alışkanlıklarını değerlendirmek için tablo yorumlama, Teknofest festivali başvuru sayılarını kök yaprak gösterimi ile analiz etme ve Ercan'ın kızları Anka ve Duha'nın harcamaları üzerinden pratik örnekler.","Video ayrıca finansal okuryazarlık kavramını da içermekte olup, Aybüke ve babasının bilgisayar fiyatlarını takip etme örneği üzerinden veri yorumlama teknikleri gösterilmektedir. Her etkinlik için adım adım çözüm yöntemleri ve yorumlama teknikleri detaylı olarak anlatılmaktadır."]},"endTime":1945,"title":"İstatistik Dersinde Veri Yorumlama ve Merkezi Eğilim Ölçüleri","beginTime":0}],"fullResult":[{"index":0,"title":"Sonuçların Yorumlanması","list":{"type":"unordered","items":["Ders kitabından \"sonuçları yorumlama\" konusuna devam ediliyor, bu konu kolay olsa da en önemli konulardan biridir.","Aritmetik ortalama, tepeler, ortanca ve açıklık gibi kavramların sorularda nasıl kullanılacağı ve problemlerin nasıl çözüleceği çalışılacaktır."]},"beginTime":6,"endTime":36,"href":"/video/preview/14487194893366907809?parent-reqid=1769502989319675-5024056911704190247-balancer-l7leveler-kubr-yp-vla-34-BAL&text=MathiXD94&t=6&ask_summarization=1"},{"index":1,"title":"Türkiye'nin Nüfus Değişimi","list":{"type":"unordered","items":["Türkiye'nin 1927, 1940, 1960, 1980, 2000 ve 2012 yıllarındaki kırsal ve kentsel nüfus verileri inceleniyor.","Yıllar geçtikçe kentsel nüfus kırsal 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kitap)."]},"beginTime":254,"endTime":593,"href":"/video/preview/14487194893366907809?parent-reqid=1769502989319675-5024056911704190247-balancer-l7leveler-kubr-yp-vla-34-BAL&text=MathiXD94&t=254&ask_summarization=1"},{"index":3,"title":"Teknofest Festivali","list":{"type":"unordered","items":["Teknofest, Türkiye'de milli teknolojinin geliştirilmesi konusunda kritik rol oynayan kuruluşların paydaşlığıyla düzenlenen Türkiye'nin ilk ve tek havacılık, uzay ve teknoloji festivalidir.","İlk 2018'de gerçekleştirilen Teknofest, teknoloji yarışmaları, hava gösterileri, konserler ve söyleşi gibi faaliyetler düzenlemektedir.","Bir ilin merkez ilçelerindeki öğrencilerin Teknofest festivaline üç farklı kategoride yaptıkları başvuru sayıları kök yaprak gösterimi ile gösterilmiştir."]},"beginTime":593,"endTime":703,"href":"/video/preview/14487194893366907809?parent-reqid=1769502989319675-5024056911704190247-balancer-l7leveler-kubr-yp-vla-34-BAL&text=MathiXD94&t=593&ask_summarization=1"},{"index":4,"title":"Merkezi Eğilim Ölçüleri","list":{"type":"unordered","items":["Veriler çok büyük veya çok küçük değerlerden oluşmuyorsa ve dağılmadığı için aritmetik ortalama kullanılabilir.","Verilerde çok fazla tekrar eden sayı varsa (tepe değeri) tepe değeri kullanmak mantıklıdır.","Veriler birbirine yakın değerlerden oluşuyorsa ortanca veya aritmetik ortalama kullanılabilir."]},"beginTime":711,"endTime":894,"href":"/video/preview/14487194893366907809?parent-reqid=1769502989319675-5024056911704190247-balancer-l7leveler-kubr-yp-vla-34-BAL&text=MathiXD94&t=711&ask_summarization=1"},{"index":5,"title":"Merkezi Eğilim Ölçüleri Hakkında Bilgiler","list":{"type":"unordered","items":["Bir veri setinin merkezi veri setinin bir eleman olmak zorunda değildir.","Bir veri setinin merkezi veri setinde bir bölgeyi gösterir.","Küçükten büyüğe sıralanmış verilerin merkezini temsil eden sayının tespitinde ilk ve son sıradaki verilerin etkisi azdır."]},"beginTime":894,"endTime":940,"href":"/video/preview/14487194893366907809?parent-reqid=1769502989319675-5024056911704190247-balancer-l7leveler-kubr-yp-vla-34-BAL&text=MathiXD94&t=894&ask_summarization=1"},{"index":6,"title":"Anka ve Duha'nın Harcamaları","list":{"type":"unordered","items":["Ercan Bey'in iki kızı Anka ve Duha'ya her gün 100 TL harçlık vermektedir.","Anka harçlığını okul kantininde, Duha ise kırtasiyede ve kültürel etkinliklerde harcamaktadır.","Ercan Bey, kızlarına harçlık verirken bilinçli tüketim, tasarruf yapma ve birikim yapabilme alışkanlıklarını kazandırmayı amaçlamaktadır."]},"beginTime":940,"endTime":985,"href":"/video/preview/14487194893366907809?parent-reqid=1769502989319675-5024056911704190247-balancer-l7leveler-kubr-yp-vla-34-BAL&text=MathiXD94&t=940&ask_summarization=1"},{"index":7,"title":"Harcama Verileri ve Merkezi Eğilim Ölçüleri","list":{"type":"unordered","items":["Anka'nın günlük harcama miktarı aritmetik ortalaması 35 TL, Duha'nın ise 30 TL'dir.","Duha'nın harcama verileri dengeli olmadığı için ortanca ölçüsü kullanılmalıdır.","Anka'nın harcama verileri daha dengeli olduğu için aritmetik ortalama kullanılabilir."]},"beginTime":985,"endTime":1209,"href":"/video/preview/14487194893366907809?parent-reqid=1769502989319675-5024056911704190247-balancer-l7leveler-kubr-yp-vla-34-BAL&text=MathiXD94&t=985&ask_summarization=1"},{"index":8,"title":"Biriktirilen Para Miktarları","list":{"type":"unordered","items":["Anka'nın biriktirdiği günlük para miktarının aritmetik ortalaması 65 TL'dir.","Duha'nın biriktirdiği günlük para miktarının aritmetik ortalaması 70 TL'dir.","Duha'nın biriktirdiği para miktarı daha dengeli olmadığı için ortanca ölçüsü kullanılmalıdır.","Anka'nın biriktirdiği para miktarı daha dengeli olduğu için aritmetik ortalama kullanılabilir."]},"beginTime":1209,"endTime":1373,"href":"/video/preview/14487194893366907809?parent-reqid=1769502989319675-5024056911704190247-balancer-l7leveler-kubr-yp-vla-34-BAL&text=MathiXD94&t=1209&ask_summarization=1"},{"index":9,"title":"Veri Setlerinin Dağılımı ve Eğilim Ölçüleri","list":{"type":"unordered","items":["Altı A sınıfındaki kız ve erkek öğrencilerin matematik derslerinden aldığı notlar inceleniyor.","Kızların notlarında büyük uçurum olduğu için ortanca ile temsil edilmeli, erkeklerin notlarında ise ortalama kullanılmalı.","Bilinçli harcama etkinliğinde sınıf içindeki arkadaşların kitap alma sıklıklarını öğrenmek için bir anket yapılması gerekiyor."]},"beginTime":1375,"endTime":1470,"href":"/video/preview/14487194893366907809?parent-reqid=1769502989319675-5024056911704190247-balancer-l7leveler-kubr-yp-vla-34-BAL&text=MathiXD94&t=1375&ask_summarization=1"},{"index":10,"title":"Finansal Okuryazarlık Kavramı","list":{"type":"unordered","items":["Finansal okuryazarlık, insanların finansal kararlar alırken gerekli bilgilere sahip olma, bu bilgileri anlama ve değerlendirme yeteneği olarak tanımlanabilir.","Finansal okuryazarlık, bireylerin gelecekteki ihtiyaçlarını düşünerek mevcut paralarını ve kaynakların nasıl yönetileceğini bilmesi de içerir.","Aybüke'nin babası, bilgisayar almak isteyen Aybüke'ye yıl içinde bilgisayarın fiyatını takip etmesini ve en uygun satın alma zamanını belirlemesini görev verdi."]},"beginTime":1470,"endTime":1540,"href":"/video/preview/14487194893366907809?parent-reqid=1769502989319675-5024056911704190247-balancer-l7leveler-kubr-yp-vla-34-BAL&text=MathiXD94&t=1470&ask_summarization=1"},{"index":11,"title":"Bilgisayar Fiyatlarının Analizi","list":{"type":"unordered","items":["Aybüke, bilgisayarın fiyatlarını etkileyen değişimleri izlemek için çeşitli genel aletlerini araştırdı ve farklı zamanlarda bilgisayarın fiyatları ile ilgili verileri topladı.","İlk on ay içinde bilgisayarın ortalama fiyatı 12.410 TL olarak hesaplandı.","İlk on ay içinde bilgisayarın en sık tekrar eden fiyatları 12.500 TL, 12.600 TL ve 12.200 TL olarak bulundu."]},"beginTime":1540,"endTime":1676,"href":"/video/preview/14487194893366907809?parent-reqid=1769502989319675-5024056911704190247-balancer-l7leveler-kubr-yp-vla-34-BAL&text=MathiXD94&t=1540&ask_summarization=1"},{"index":12,"title":"Veri Setinin Diğer Özellikleri","list":{"type":"unordered","items":["İlk on ay içinde bilgisayarın TL cinsinden fiyatı küçükten büyüğe sıralandığında ortadaki değer 12.450 TL olarak hesaplandı.","İlk on ay içinde bilgisayarın en düşük değeri 12.100 TL, en yüksek değeri 12.700 TL ve bu iki değer arasındaki fark 600 TL olarak bulundu.","Bilgisayarın ilk on ay içinde alınacak en uygun zamanı Ekim ayı olarak belirlendi ve bu zamandaki fiyatı merkezi eğilim ölçülerinden herhangi birinin değeri ile örtüşüyor."]},"beginTime":1676,"endTime":1941,"href":"/video/preview/14487194893366907809?parent-reqid=1769502989319675-5024056911704190247-balancer-l7leveler-kubr-yp-vla-34-BAL&text=MathiXD94&t=1676&ask_summarization=1"}],"linkTemplate":"/video/preview/14487194893366907809?parent-reqid=1769502989319675-5024056911704190247-balancer-l7leveler-kubr-yp-vla-34-BAL&text=MathiXD94&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"6. 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Konuşmacı, bozuk bir EGR valfi göstererek konuyu anlatmaktadır.","Video, EGR valfinin ne olduğu, işlevi ve önemi hakkında detaylı bilgiler sunmaktadır. EGR valfinin egzoz emisyon değerlerini düşürme, yanma sıcaklığını düşürme ve yakıt tasarrufu sağlama gibi temel görevleri açıklanmaktadır. Ayrıca, EGR valfinin bozulması durumunda ortaya çıkabilecek sorunlar (motor arıza lambası yanması, egzoz emisyon değerlerinin yükselmesi, yakıt tüketiminin artması, motorda vuruntu oluşması gibi) ve EGR valfinin temizlenmesi veya iptali konuları ele alınmaktadır."]},"endTime":289,"title":"EGR Valfi Nedir ve Ne İşe Yarar?","beginTime":0}],"fullResult":[{"index":0,"title":"EGR Valfi Nedir ve Ne İşe Yarar","list":{"type":"unordered","items":["EGR valfi, dizel ve benzinli araçlarda bulunan, egzoz emisyon değerlerini düşürme konusunda önemli görevlere sahip bir parçadır.","EGR valfinin amacı, silindirlerden atılan egzoz gazının ortalama yüzde on miktarının temiz havayla karıştırılarak yanma odasına verilmesi ve bu sayede verimin arttırılmasıdır.","EGR valfi, egzozdaki nitrik oksit ve azot oksit gibi zehirli gazları tekrar yanmaya elverişli hale getirerek egzoz gazının zararını minimuma indirir."]},"beginTime":0,"endTime":84,"href":"/video/preview/3087007657307706961?parent-reqid=1769502989319675-5024056911704190247-balancer-l7leveler-kubr-yp-vla-34-BAL&text=MathiXD94&t=0&ask_summarization=1"},{"index":1,"title":"EGR Valfinin Temel Amaçları","list":{"type":"unordered","items":["EGR valfinin en büyük amacı egzoz emisyon değerlerini düşürmek ve silindir içerisindeki yanma sıcaklığını düşürerek motorun daha sağlıklı çalışmasını sağlamaktır.","EGR valfi, egzoz gazının tekrar yanmasını sağlayarak verimi artırır ve bu sayede yakıt tasarrufu elde edilir."]},"beginTime":84,"endTime":112,"href":"/video/preview/3087007657307706961?parent-reqid=1769502989319675-5024056911704190247-balancer-l7leveler-kubr-yp-vla-34-BAL&text=MathiXD94&t=84&ask_summarization=1"},{"index":2,"title":"EGR Valfi Bozulduğunda Oluşan Sorunlar","list":{"type":"unordered","items":["EGR valfi bozulduğunda arıza lambası yanar ve egzoz emisyon değerleri yükselir.","Motor çalışma sıcaklığı artar, yakıt tüketimi artar ve araçta vuruntu, sarsıntılı çalışma ve tekleme oluşur.","Araçta düzensiz rölanti ve performans kaybı yaşanan araçta uzun süreli kullanım sonucunda motor ve subapla ilgili sorunlar ortaya çıkar."]},"beginTime":112,"endTime":208,"href":"/video/preview/3087007657307706961?parent-reqid=1769502989319675-5024056911704190247-balancer-l7leveler-kubr-yp-vla-34-BAL&text=MathiXD94&t=112&ask_summarization=1"},{"index":3,"title":"EGR Valfi Sorunları ve Çözümleri","list":{"type":"unordered","items":["EGR valfinin tıkandığı gibi açık kalması da problemlere yol açar.","Kurumdan dolayı kirlenen EGR valfi temizlenebilir, ancak çok fazla kurum biriktiyse ve taşlaşmaya dönmüşse değiştirilmesi gerekir.","EGR valfinin iptali tavsiye edilmez çünkü bu durumda yakıtla ve egzoz emisyonla ilgili büyük sorunlar ortaya çıkar."]},"beginTime":208,"endTime":287,"href":"/video/preview/3087007657307706961?parent-reqid=1769502989319675-5024056911704190247-balancer-l7leveler-kubr-yp-vla-34-BAL&text=MathiXD94&t=208&ask_summarization=1"}],"linkTemplate":"/video/preview/3087007657307706961?parent-reqid=1769502989319675-5024056911704190247-balancer-l7leveler-kubr-yp-vla-34-BAL&text=MathiXD94&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"EGR Valfi Nedir? Bozuk EGR Valfi Araçta Nasıl Anlaşılır ? Hızlı ve etkili çözüm 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