Average - Study Mode

[#206] The mean of 20 items is 55. If two items 45 and 30 are removed, the new mean of the remaining items is :
Correct Answer

(C) 56.9

Explanation

Solution: According to the question, Mean of 20 items is = 55 Sum of 20 items is = 55 × 20 = 1100 Two items removed = 45 + 30 = 75 Now, sum of 18 items = 1100 - 75 = 1025 ∴ Average = $$frac{1025}{18}$$ = 56.9

[#207] The average weight of a group of 20 boys was calculated to be 89.4 kg and it was later discovered that one weight was misread as 78 kg instead of 87 kg. The correct average weight is -
Correct Answer

(D) 89.85 kg

Explanation

Solution: According to the question, Average weight of a 20 boys = 89.4 kg Sum of a weight of 20 boys = 89.4 × 20 = 1788 kg It was later discovered that one weight was misread as 78 kg instead of 87 kg. ∴ Difference = 87 - 78 = 9 kg ∴ Actual sum of a weight of 20 boys = 1788 + 9 = 1797 kg. Actual average = $$frac{1797}{20}$$ xa0 = 89.85 kg

[#208] A batsman in his 12 th innings makes a score of 63 runs and there by increases his average score by 2. What is his average after the 12 th innings ?
Correct Answer

(C) 41

Explanation

Solution: Let the average score till his 11 innings = x According to the question, ⇒ $$frac{11x + 63}{12}$$ xa0 = x + 2 ⇒ 11x + 63 = 12x + 24 ⇒ x = 39 12 th innings average = 39 + 2 = 41

[#209] Out of 10 teachers of a school, one teacher retires and in place of him a new teacher 25 years old joins. As a result of it average age of the teachers reduces by 3 years. Age of the retired teacher (in years) is -
Correct Answer

(A) 55

Explanation

Solution: Age of retired teacher = 25 + (10 × 3) = 25 + 30 = 55 years

[#210] If the mean of 4 observations is 20, when a constant 'c' is added to each observation, the mean becomes 22. The value of c is :
Correct Answer

(C) 2

Explanation

Solution: Let the four observations are = a, b, d, e According to the question, $$frac{a + b + e + d}{4}$$ xa0 = 20.....(i) $$frac{a + c + b + c + e + c + d + c}{4}$$ xa0 xa0 = 22 $$frac{4c + (a + b + e + d)}{4}$$ xa0 xa0 = 22 $$frac{4c}{4}$$ + 20 = 22 c = 2