The sum of 11 numbers is 660. Find their average.
60
Finding the Average of 11 Numbers
The question asks us to find the average of a set of 11 numbers, given their total sum.
The average of a set of numbers is calculated by dividing the sum of all the numbers by the total count of numbers in the set.
The formula for the average is:
\text{Average} = \frac{\text{Sum of numbers}}{\text{Number of numbers}}
In this problem, we are given:
- The sum of the 11 numbers is 660.
- The total number of numbers is 11.
Now, let's substitute these values into the average formula:
\text{Average} = \frac{660}{11}
Performing the division:
\frac{660}{11} = 60
So, the average of the 11 numbers is 60.
Step-by-Step Average Calculation
- Identify the given sum of numbers: Sum = 660.
- Identify the total count of numbers: Count = 11.
- Recall the average formula: Average = Sum / Count.
- Substitute the given values: Average = 660 / 11.
- Calculate the result: Average = 60.
Therefore, the average of the 11 numbers is 60.
Revision Table: Key Concepts
| Concept | Description | Formula |
|---|---|---|
| Average (Mean) | A measure of central tendency; sum of values divided by count. | \(\text{Average} = \frac{\text{Sum}}{\text{Count}}\) |
| Sum | The total obtained by adding all the numbers in a set. | - |
| Count | The total number of items or values in a set. | - |
Additional Information on Averages
The average, also known as the arithmetic mean, is one of the most common ways to represent a typical value from a set of data. It is sensitive to extreme values (outliers). Besides the mean, other types of averages include the median (the middle value when data is ordered) and the mode (the most frequent value).
Understanding how to calculate the average is fundamental in various fields, including statistics, finance, and everyday life for things like calculating average speed, average scores, or average expenses.
When working with averages, always ensure you have the correct total sum and the correct count of items.
Important Questions from Average
The average of 28 numbers is 77. The average of first 14 numbers is 74 and the average of last 15 numbers is 84. If the 14 th number is excluded, then what is the average of remaining numbers? (correct to one decimal places)
24 students collected money for donation. The average contribution was Rs. 50. Later on, their teacher also contributed some money. Now the average contribution is Rs. 56. The teacher’s contribution is:
Out of 6 numbers, the sum of the first 5 numbers is 7 times the 6 th number. If their average is 136, then the 6 th number is:
The average of five numbers is 30. If one number is excluded, then average becomes 31. What is the excluded number?
The average weight of 49 students in a class is 39 kg. Seven of them whose average weight is 40 kg leave the class and other seven students whose average weight is 54 kg join the class. What is the new average weight (in kg) of the class?
