निम्नलिखित आँकड़ों पर विचार कीजिए:
- लड़कियाँ: अंग्रेजी में माध्य प्राप्तांक = 9, हिन्दी में माध्य प्राप्तांक = 8
- लड़के: अंग्रेजी में माध्य प्राप्तांक = 8, हिन्दी में माध्य प्राप्तांक = 7
- कुल माध्य प्राप्तांक: अंग्रेजी = 8.8, हिन्दी = x
उपयुक्त सारणी में x का मान क्या है?
सही उत्तर: (b) 7.6
मान लेते हैं कि लड़कियों की संख्या G और लड़कों की संख्या B है। अंग्रेजी के कुल प्राप्तांकों से: (9G + 8B)/(G + B) = 8.8, जिससे हल करने पर G = 4B प्राप्त होता है (अर्थात G : B = 4 : 1)। अब हिन्दी के कुल माध्य प्राप्तांक x के लिए: x = (8G + 7B) / (G + B)। G और B के मान रखने पर: (8(4) + 7(1)) / (4 + 1) = 39 / 5 = 7.8। अतः x का मान 7.8 है।
In English (Question & Model Answer)
Consider the following data:
- Girls: Average marks in English = 9, Average marks in Hindi = 8
- Boys: Average marks in English = 8, Average marks in Hindi = 7
- Overall average marks: English = 8.8, Hindi = x
What is the value of x in the above table?
Correct Option: (b) 7.6
Let the number of girls be G and the number of boys be B. From the data given: Girls' average in English = 9, Hindi = 8. Boys' average in English = 8, Hindi = 7. Overall average in English = 8.8. Let's use the weighted average formula for English: (9G + 8B) / (G + B) = 8.8. Simplifying: 9G + 8B = 8.8G + 8.8B => 0.2G = 0.8B => G / B = 0.8 / 0.2 = 4 / 1. Thus, the ratio of girls to boys is G : B = 4 : 1. Now, let's find the overall average in Hindi, denoted by x: x = (8G + 7B) / (G + B). Since G = 4k and B = k, substitute these into the equation: x = (8(4) + 7(1)) / (4 + 1) = (32 + 7) / 5 = 39 / 5 = 7.8? Wait, let's recalculate carefully: 32 + 7 = 39, 39 / 5 = 7.8. Wait, let's check option (a) which is 7.8. Let's re-verify the English weighted average: (9G + 8B) / (G + B) = 8.8 => 9G + 8B = 8.8G + 8.8B => 0.2G = 0.8B => G = 4B. Correct. Now Hindi average: (8G + 7B) / (G + B) = (8(4B) + 7B) / (5B) = (32B + 7B) / 5B = 39B / 5B = 39 / 5 = 7.8. Therefore, x = 7.8. Option (a) is correct.