Question
Download Solution PDFThe average age of 30 students of a school was found to be 19 yrs. If a student of age 26 left and another student of age 20 yrs joined then find the new average age.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
No. of students = 30
Average age of students = 19 yrs.
Formula Used:
Average = Sum/Number
Concept Used:
Change in Average = (Change in Sum)/Total Number.
Calculation:
When the student of 26 years was present, then
Sum of the age of students = Average age of students × Total Number of students.
Sum of the age of students = 19 × 30 = 570
Now,
When the student of 26 years was replaced by a student of age 20 years, then
New Sum of the age of students = 570 - 6 = 564
⇒ [∵ the student who replaced had 6yrs less age than the student who left, so the sum got reduced by 6 yrs.]
So, the New Average = (New Sum)/(Total Number of students)
∴ New Average = 564/30 = 18.8 years.
Alternate Method⇒ New Average = Old Average - Change in Average.
⇒ We are subtracting here because the sum has reduced from before, therefore the New Average will also decrease.
⇒ New Average = 19 - (6/30) → [ Change in Average = (Change in Sum)/Total Number.]
⇒ New Average = 19 - 0.2 = 18.8 years.
Last updated on Jul 7, 2025
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