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 height of 20 students of class 8 is 152 cm and the average height of 15 students of class 9 is 168 cm. What is the average height (to the nearest cm) of the students of both classes?
The average of 4, 6, 8, 12 and x is 7 and the average of x, 9, 13, 15 and y is 9. What is the value of 2x - 3y?
The average weight of 20 girls in a school was 52 kg. Two new students of weight 54 kg and 50 kg were admitted. The ratio of this new average to the old one is:
If the average of two numbers is 13 and the square root of their product is 12, then the difference between the numbers is:
If the average of 5 consecutive odd integers in increasing order is 11 , then the average of the last 3 of them is:
