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Mean

Working with data

Japanese school year: Elementary 5

What you learn

Learn how to calculate the average by leveling out multiple numerical values, and understand how to interpret it. The mean is widely used to represent the central tendency of test scores or experimental observations. Confident skills in multi-digit addition and division will help you solve problems accurately.

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Key points

This formula calculates the arithmetic mean xˉ\bar{x} of a dataset. Divide the sum of all values (x1x_1 through xnx_n) by the total number of values nn.

xˉ=x1+x2+⋯+xnn\bar{x} = \frac{x_1 + x_2 + \dots + x_n}{n}

This formula calculates the total sum of data from the mean and count. Multiplying the mean xˉ\bar{x} by the number of items nn gives the sum of all values (x1+⋯+xnx_1 + \dots + x_n).

x1+x2+⋯+xn=nxˉx_1 + x_2 + \dots + x_n = n\bar{x}

This formula expresses the mean xˉ\bar{x} compactly using the summation symbol ∑\sum (sigma). ∑i=1nxi\sum_{i=1}^n x_i denotes the sum of values from x1x_1 to xnx_n, which is then divided by nn.

xˉ=1n∑i=1nxi\bar{x} = \frac{1}{n}\sum_{i=1}^n x_i

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