Question
The average of 13 numbers is 8. If each number is multiplied by 7, then what will the new average be:
The correct answer is
56
Average Property Explained
A key property of averages states that if every number in a dataset is multiplied by a constant value, the average of the dataset is also multiplied by that same constant.
Calculating the New Average
Let the original average of the 13 numbers be Aoriginal. We are given that Aoriginal = 8.
Each number is multiplied by a constant, k = 7.
According to the property of averages, the new average, Anew, is calculated as:
$ A_{new} = A_{original} \times k $
Substituting the given values:
$ A_{new} = 8 \times 7 $
$ A_{new} = 56 $
Therefore, the new average will be 56.
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Important Questions from Average (Notes)
- The average age of a group of boys and girls is 18 years. If the average age of boys is 20 years and that of girls is 15 years, then what is the percentage of boys in the group?
- There are 78 members in group A, 22 members in group B and 34 members in group C. All the members of these groups went to a restaurant. The average amounts spent on each member of groups A, B and C are ₹136, ₹383 and ₹457, respectively. The overall average amount (in ₹) spent per member is:
- If the average of p numbers is $q^2$ and that of q numbers is $p^2$, then the average of (p + q) numbers is :
- The average of 101 consecutive odd numbers is 303. Find the largest number.
- For three consecutive years, the cost of a product were Rs. $134$ per litre, Rs.$268$ per litre and Rs.$335$ per litre respectively. If a common man spends an average of Rs. $14740$ per year on that product, then what is the average cost of that product per litre for the three years? (In Rs. - upto two decimals)
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