The concept of average is one that is widely used in many areas of life, from mathematics and statistics to everyday conversations. At its core, the average is a measure of central tendency that tells us what the typical value is in a set of data. In this article, we will explore what the average is, how it is calculated, and some of the important uses of averages.
What is the Average?
The average is a statistical measure that represents the typical value of a set of data. It is also known as the mean and is calculated by adding up all the values in a data set and then dividing by the number of values in the set. For example, if we have a data set of {2, 4, 6, 8, 10}, we would add up all the values (2 + 4 + 6 + 8 + 10 = 30) and then divide by the number of values in the set (5), giving us an average of 6.
How is the Average Calculated?
To calculate the average of a data set, we follow a simple formula: add up all the values in the set and then divide by the number of values in the set. This formula can be written mathematically as:
Average = (sum of all values in the set) / (number of values in the set)
For example, if we have a data set of {2, 4, 6, 8, 10}, we would add up all the values (2 + 4 + 6 + 8 + 10 = 30) and then divide by the number of values in the set (5), giving us an average of 6.
Averages are also useful for comparing different data sets. For example, if we have two sets of data that represent the performance of two different companies, we can calculate the average revenue and compare them to see which company is doing better.
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The average of three numbers is 20. If one number is 15 and another number is 25, what is the third number? Solution: Let x be the third number. Then, we have (15 + 25 + x) / 3 = 20. Solving for x, we get x = 20. Therefore, the third number is 20.
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The average of five numbers is 12. If one number is 10 and another number is 15, what is the sum of the other three numbers? Solution: Let the sum of the other three numbers be x. Then, we have (10 + 15 + x) / 5 = 12. Solving for x, we get x = 48. Therefore, the sum of the other three numbers is 48.
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The average weight of 10 students is 60 kg. If the weight of one student is 70 kg, what is the new average weight if he is replaced by a student weighing 50 kg? Solution: The sum of the weights of the 10 students is 600 kg. If we replace one student weighing 70 kg with another student weighing 50 kg, the total weight becomes 580 kg. Therefore, the new average weight is 580 / 10 = 58 kg.
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The average of four numbers is 25. If one number is 30, what is the average of the remaining three numbers? Solution: The sum of the four numbers is 100. If one number is 30, the sum of the remaining three numbers is 100 - 30 = 70. Therefore, the average of the remaining three numbers is 70 / 3 = 23.33 (rounded to two decimal places).
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The average of six numbers is 18. If the average of the first three numbers is 15 and the average of the last three numbers is 21, what is the fourth number? Solution: Let x be the fourth number. Then, we have (15 + 21 + x) / 3 = 18. Solving for x, we get x = 24. Therefore, the fourth number is 24.
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The average age of a family of five members is 40 years. If the age of the youngest member is 20 years, what is the average age of the other four members? Solution: The sum of the ages of the five members is 200 years. If the age of the youngest member is 20 years, the sum of the ages of the other four members is 200 - 20 = 180 years. Therefore, the average age of the other four members is 180 / 4 = 45 years.
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The average of five consecutive even numbers is 24. What is the largest of these numbers? Solution: Let x be the first even number. Then, the five consecutive even numbers are x, x+2, x+4, x+6, and x+8. We have (x + (x+2) + (x+4) + (x+6) + (x+8)) / 5 = 24. Solving for x, we get x = 20. Therefore, the largest of these numbers is x + 8 = 28.
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The average of four numbers is 16. If one number is 20 and another number is 12, what is the average of the remaining two numbers? Solution: The sum of the four numbers is 64. If one number is 20 and another number is 12, the sum of the remaining two numbers is 64 - 20 - 12 = 32. Therefore, the average of the
