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Find the Average of all multiples of 3 between 100 and 1000
The average of all multiples of 3 between 100 and 1000 is 550.5.
To find the average of all multiples of 3 between 100 and 1000, we need to find the sum of these multiples and then divide by the count of multiples.
First, let’s find the count of multiples of 3 between 100 and 1000:
The smallest multiple of 3 greater than or equal to 100 is 102. The largest multiple of 3 less than or equal to 1000 is 999. To find the count, we can use the formula for the count of integers in an arithmetic sequence:
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Count = (Largest Term – Smallest Term) / Common Difference + 1
In this case, the common difference is 3.
Count = (999 – 102) / 3 + 1
Count = 897 / 3 + 1
Count = 299 + 1
Count = 300
Now, let’s find the sum of these multiples:
Sum = (n / 2) * (First Term + Last Term)
Sum = (300 / 2) * (102 + 999)
Sum = 150 * 1101
Sum = 165150
Finally, we’ll find the average:
Average = Sum / Count
Average = 165150 / 300
Average = 550.5
So, the average of all multiples of 3 between 100 and 1000 is 550.5.
What is an Average in Mathematics?
In mathematics, an average is a measure that represents a central or typical value of a set of numbers. There are several types of averages commonly used:
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Arithmetic Mean: The arithmetic mean is calculated by summing up all the numbers in a set and then dividing by the count of numbers.
Arithmetic Mean = (1/n) * Σ(xi)
Where ‘n’ is the number of values, and ‘xi’ are the individual values.
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Median: The median is the middle value of a sorted set of numbers. If there is an even number of observations, the median is the average of the two middle numbers.
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Mode: The mode is the value that appears most frequently in a dataset.
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Geometric Mean: The geometric mean is calculated by taking the nth root of the product of a set of values, where ‘n’ is the count of the values.
Geometric Mean = nth root of (x1 * x2 * … * xn)
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Harmonic Mean: The harmonic mean is the reciprocal of the arithmetic mean of the reciprocals of a set of values.
Harmonic Mean = n / ((1/x1) + (1/x2) + … + (1/xn))
Each type of average has its own characteristics and is useful in different situations depending on the nature of the data and the specific analysis being performed.
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Categories: Math
