Average [औसत] - 02

Question: The average weight of 8 persons increases by 2.5 Kg., when one of them, whose weight is 56 Kg., is replaced by a new person, what could be the weight of the new persons? [8 लोगों का औसत वजन 2.5 किग्रा से बढ़ जाता है, जब उनमें से 56 किग्रा के एक व्यक्ति की जगह पर एक नया व्यक्ति आ जाता है. नए व्यक्ति का वजन क्या है?]  [Ans. (c) 76 Kg]  

(a) 66 Kg   (b) 75 Kg   (c) 76 Kg   (d) 86 Kg   (e) none of these

Detailed Explanation: When items of a group are equally distributed, then each value becomes equal. That each equal value is said to be “Average”.  When any value of the group is removed and a new value added; then if new value is equal to the removed value, then average is not affected. But, it the new value is more than the removed value, then average increases. If the new value is less than the removed value, then average decreases.

By substitution, if the average of the group increases or decreases, then the net change is added to the new value, or subtracted from the new value respectively.  

Total increase in weight = 8 × 2.5 = 20 kg

Weight of new person = 56 + 20) kg = 76 kg Ans.