Average
An average is a single number that represents a group of different values. It is also called the arithmetic mean. Think of it as sharing everything equally among a group. If five friends have different amounts of chocolate, the average is how many chocolates each would get if they shared them all equally. The basic formula is: Average = (Sum of all values) divided by (Total number of items). For example, if you score 40, 50, and 60 marks in three tests, the total marks are 150.
Concepts (3)
When a person joins or leaves a group, the average changes. To find the value of the new person: New Value = Old Average + (Number of people now × Change in Average). Example: Average weight of 5 people is 60kg.
When a person joins or leaves a group, the average changes. To find the value of the new person: New Value = Old Average + (Number of people now × Change in Average). Example: Average weight of 5 people is 60kg. A new person joins and average becomes 62kg. New weight = 60 + (6 × 2) = 72kg.
In a sequence where the gap between numbers is the same (like 2, 4, 6, 8), the average is the middle term. If there are two middle terms, it is the average of those two. A quick formula is: Average = (First Term + Last Term) / 2.
In a sequence where the gap between numbers is the same (like 2, 4, 6, 8), the average is the middle term. If there are two middle terms, it is the average of those two. A quick formula is: Average = (First Term + Last Term) / 2. Example: To find the average of numbers from 1 to 99, calculate (1 + 99) / 2 = 50.
This method helps solve hard problems without big multiplications. We pick an 'assumed average' and see how much each number is above or below it. The sum of these differences (deviations) must be zero for the true average.
This method helps solve hard problems without big multiplications. We pick an 'assumed average' and see how much each number is above or below it. The sum of these differences (deviations) must be zero for the true average. Example: If the average of 10, 20, and 30 is 20, the deviations are -10, 0, and +10. The sum is 0.
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