Average (Notes) New
An average, or more accurately an arithmetic mean, is the sum of n different data divided by n.
For example, if a batsman scores 41, 51 and 43 runs in first, second and third match respectively,
then his average runs in 3 matches is equal to =
Problem=1 : The average age of 30 boys of a class is equal to 14 years. When the age of the class teacher is included, the average become 15 years, find the age of the class teacher.
Problem 2 : The average weight of 4 men is increased by 3kg when one of them who weighs 120kg is replaced by another man. What is the weight of the new man?
Problem 3 : The average of marks obtained by 120 candidates in a certain examination is 35. If the average marks of passed candidates is 39 and that of the failed candidates is 15, what is the number of candidates who passed the examination?
Solution : Short trick
Problem : 4 The average of 11 results is 50. If the average of first six results is 49 and that of last six is 52, find the sixth result.
Problem :5 The average of 11 results is 30, that of the first five is 25 and that of the last five is 28. Find the value of the 6th result.
Problem 6: The average age of 8 persons in a committee is increased by 2 years when two men aged 35 years and 45 years are substituted by two women. Find the average age of two women.
Problem 7 : A man bought 13 shirts of Rs.50 each, 15 shirts of Rs.60 each and 12 pairs of shoes at Rs. 65 a pair. Find the average value of each article.
Problem 8: In a class, there are 20 boys whose average age is decreased by 2 months, when one boy aged 18 years is replaced by a new boy. Find the age of a new boy.
Sol: Age of the new boy= Age of the boy who left – No. of persons × Decrease in average age
Problem 9 : A batsman in his 17th innings makes a score of 85, and thereby increase his average by 3. What is his average after 17 innings?
Sol: Let the average score after 16th innings be x.