Find the average of the following sets of numbers. 693, 456, 876, 532, 934, 691, 596, 398, 682
650.89
Calculating the Average of a Set of Numbers
To find the average (also known as the mean) of a set of numbers, we need to perform two main steps:
- Add up all the numbers in the set.
- Divide the total sum by the count of numbers in the set.
The set of numbers given is: 693, 456, 876, 532, 934, 691, 596, 398, 682.
Step 1: Sum the Numbers
Let's add all the numbers together:
Sum $= 693 + 456 + 876 + 532 + 934 + 691 + 596 + 398 + 682$
Sum $= 1149 + 876 + 532 + 934 + 691 + 596 + 398 + 682$
Sum $= 2025 + 532 + 934 + 691 + 596 + 398 + 682$
Sum $= 2557 + 934 + 691 + 596 + 398 + 682$
Sum $= 3491 + 691 + 596 + 398 + 682$
Sum $= 4182 + 596 + 398 + 682$
Sum $= 4778 + 398 + 682$
Sum $= 5176 + 682$
Sum $= 5858$
The sum of the given numbers is 5858.
Step 2: Count the Numbers
Next, we count how many numbers are in the set.
There are 9 numbers in the set (693, 456, 876, 532, 934, 691, 596, 398, 682).
Count $= 9$
Step 3: Calculate the Average
Now, we divide the sum by the count:
Average $= \frac{\text{Sum}}{\text{Count}}$
Average $= \frac{5858}{9}$
Let's perform the division:
| Calculation | Result |
|---|---|
| $5858 \div 9$ | $650.888...$ |
Rounding the result to two decimal places, we get approximately 650.89.
Therefore, the average of the given set of numbers is approximately 650.89.
Revision Table: Key Concepts of Average
| Concept | Definition | Formula |
|---|---|---|
| Average (Mean) | A measure of central tendency; the sum of all values divided by the number of values. | Average $= \frac{\text{Sum of all values}}{\text{Number of values}}$ |
| Sum | The result of adding all numbers in the set. | Sum $= \text{Value}_1 + \text{Value}_2 + ... + \text{Value}_n$ |
| Count | The total number of values in the set. | Count $= n$ (where $n$ is the number of values) |
Additional Information on Measures of Central Tendency
The average, or mean, is one of several measures of central tendency used in statistics. Other common measures include the median and the mode.
- Median: The middle value in a data set that has been ordered from least to greatest. If there is an even number of values, the median is the average of the two middle values.
- Mode: The value that appears most frequently in a data set. A data set can have one mode (unimodal), more than one mode (multimodal), or no mode.
These measures help summarise data by identifying a typical or central value within a distribution.
Similar Questions
The average weight of 10 students is increased by half a kg when one of the students weighing 51 kg is replaced by a new student. Find the weight of the new student.
The average of 36 numbers was found to be 45. Later, it was detected that 84 was misread as 48. Find the correct average of the given numbers.
One quality of rice at Rs. 45 per kg is mixed with another quality at a certain rate in the ratio of 3 ∶ 2. If the mixture so formed is worth Rs. 50 per kg, what is the rate per kg of the second quality of rice?
The average weight of 15 persons is increased by 1.2 kg when one of them whose weight is 51 kg is replaced by a new man. The weight of the new man is:
There are 15 students in a class. Their average weight is 40 kg. When one student leaves the class, the average weight is 39.5 kg. What is the weight of the student who left the class (where kg means kilogram)?
In a class of 60 students, 20 are girls. The average weight of the boys in the class is 40 kg, while that of all the girls is 35 kg. What is the average weight (in kg) of the entire class (correct to two decimal places)?
In a class of 60 students, there are 35 boys. The average weight of boys is 42 kg and the average weight of the full class is 46.5 kg. Find the average weight of girls in the class.
The average weight of 12 persons increases by 3.5 kg when a new person comes in place of one of them weighing 58 kg. The weight of the new person is:
The average of the first 7 non-zero multiples of 17 is:
Find the average of the cubes of the first five natural numbers.
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:
