निम्नलिखित संख्याओं का माध्यक ज्ञात कीजिए:

59, 67, 51, 88, 23, 61, 71, 15, 39, 29

  1. 65
  2. 55
  3. 45
  4. 75

Answer (Detailed Solution Below)

Option 2 : 55
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संकल्पना:

माध्यक आरोही क्रम में संख्याओं को व्यवस्थित करने के बाद श्रृंखला की मध्य संख्या है। तत्वों की कुल संख्या n वाले एक श्रृंखला के लिए:

  • यदि n विषम है, तो माध्यक \(\rm{\left(n+1\over2\right)}^{th}\) तत्व है। 
  • यदि n सम है, तो माध्यक \(\rm{\left(n\over2\right)}^{th}\) और \(\rm\left({n\over2}+1\right)^{th}\) तत्वों का औसत है। 

गणना:

संख्याओं को आरोही क्रम में व्यवस्थित करने के बाद:

15, 23, 29, 39, 51, 59, 61, 67, 71, 88

कुल तत्व 10 हैं, इसलिए माध्यक पांचवे और छठे तत्व औसत है। 

माध्यक = \(\rm\left(51+59\over2\right)\) = 55

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