Question
Download Solution PDFप्रेक्षणों के समुच्चय का माध्य \(\bar{x}\) है। यदि प्रत्येक प्रेक्षण को k से विभाजित किया जाए और फिर 5 से बढ़ाया जाए, तो नए समुच्चय का माध्य मान होगा।
Answer (Detailed Solution Below)
Detailed Solution
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मान लीजिए a, b, c ...... प्रेक्षणों का 'n' समुच्चय है।
प्रेक्षणों के इस समुच्चय का माध्य, \(\bar{x}\) = \(a + b+ c ....... \over n\)
प्रत्येक प्रेक्षण को k से विभाजित करने और फिर उन्हें 5 से बढ़ाने के बाद, प्रेक्षणों का एक नया समुच्चय \(a \over k \) + 5, \(b \over k\) + 5, ....... है।
अतः, प्रेक्षणों के नए समुच्चय का माध्य
नया माध्य = \(\frac{{\left( {\frac{a}{k} + 5} \right) + \left( {\frac{b}{k} + 5} \right) + ......}}{n} = \frac{{\left( {\frac{a}{k} + \frac{b}{k} + ....} \right) + \left( {5n} \right)}}{n}\)
उपरोक्त पदों को पुनः व्यवस्थित करने पर, हम पाते हैं,
नया माध्य = \(\frac{{\left( {\frac{{a + b + .....}}{n}} \right) + 5k}}{k}\)
नया माध्य = \(\dfrac{\bar{x} + 5k}{k}\)
Last updated on Oct 21, 2024
-> GPSC Engineering Services 2024 Notification has been released on the official website.
-> A total of 17 Vacancies have been announced for the posts of Gujarat Engineering Service (Civil), Class-I & Class- II under various departments. Interested candidates can apply from 15th October 2024 to 30th October 2024.
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