21 से 50 के बीच सभी अभाज्य संख्याओं के माध्य और माध्यक में कितना अंतर है?

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MP Excise Constable Official Paper (Held on : 24 Feb 2023 Shift 3)
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  1. \(\frac{4}{7}\)
  2. \(\frac{8}{7}\)
  3. \(\frac{6}{7}\)
  4. \(\frac{3}{7}\)

Answer (Detailed Solution Below)

Option 2 : \(\frac{8}{7}\)
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प्रयुक्त सूत्र:

माध्य = प्रेक्षणों का योग/ प्रेक्षणों की संख्या

गणना: 

21 से 50 के बीच अभाज्य संख्याएँ निम्नलिखित हैं:

⇒ 23, 29, 31, 37, 41, 43, 47 

माध्य\(\dfrac{23 + 29 + 31 + 37 + 41 + 43 +47}{7}\)

⇒ \(\dfrac{251}{7}\) 

कुल संख्याएँ = 7 (विषम संख्या)

इसलिए, माध्यक = [(n + 1)/2]वाँ पद

⇒ [(7 + 1)/2]वाँ पद

⇒ चौथा पद = 37

माध्य और माध्यक के बीच अंतर:

⇒ 37 - \(\dfrac{251}{7}\)

\(\dfrac{259 - 251}{7}\) = \(\dfrac{8}{7}\)

सही उत्तर विकल्प 2 है।

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