Question
निम्नलिखित आँकड़ों से माध्य, माध्यिका और बहुलक की गणना करें
| कक्षा अंतराल | आवृत्ति |
|---|---|
| 3 - 4 | 3 |
| 4 - 5 | 7 |
| 5 - 6 | 22 |
| 6 - 7 | 60 |
| 7 - 8 | 85 |
| 8 - 9 | 32 |
| 9 - 10 | 8 |
ऊपर दिए गए आँकड़ों से विचरण के गुणांक की गणना करें।
Answer :
Word Count : 839
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Skip in 10
माध्य, माध्यिका, बहुलक और विचरण के गुणांक (Coefficient of Variation) की गणना हेतु पहले दिए गए वर्गों का वर्ग-मध्य (class mark) और आवश्यक सांख्यिकीय सारणी तैयार करते हैं। प्रारंभिक तालिका: | कक्षा अंतराल | आवृत्ति (f) | वर्ग मध्य (x) | f\*x | | ------------ | ----------- | ------------- | ---------- | | 3 - 4 | 3 | 3.5 | 10.5 | | 4 - 5 | 7 | 4.5 | 31.5 | | 5 - 6 | 22 | 5.5 | 121.0 | | 6 - 7 | 60 | 6.5 | 390.0 | | 7 - 8 | 85 | 7.5 | 637.5 | | 8 - 9 | 32 | 8.5 | 272.0 | | 9 - 10 | 8 | 9.5 | 76.0 | | योग (Σ) | 217 | | 1538.5 | --- ### 1. माध्य (Mean): $$ \bar{x} = \frac{\sum f x}{\sum f} = \frac{1538.5}{217} \approx 7.09 $$ --- ### 2. माध्यिका (Median): माध्यिका ज्ञात करने हेतु, कुल आवृत्ति = 217 $$ \frac{N}{2} = \frac{217}{2} = 108.5 $$ माध्यिका वर्ग वह वर्ग होगा जिसमें 108.5वां प्रेक्षण आता है। संचयी आवृत्ति सारणी: | कक्षा अंतराल | आवृत्ति (f) | संचयी आवृत्ति | | | ------------ | ----------- | ------------- | ------------------ | | 3 - 4 | 3 | 3 | | | 4 - 5 | 7 | 10 | | | 5 - 6 | 22 | 32 | | | 6 - 7 | 60 | 92 | | | 7 - 8 | 85 | 177 | ← Median Class | | 8 - 9 | 32 | 209 | | | 9 - 10 | 8 | 217 | | Median Class = 7 - 8 L = 7, F = 92, f = 85, h = 1 $$ \text{Median} = L + \left( \frac{\frac{N}{2} - F}{f} \right) \times
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