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.
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?
