Median & range

Japanese school year: Elementary 6

What you learn

Learn to find the median (the middle value or the mean of the two middle values for even data sizes) and the range (the difference between maximum and minimum). The median is a representative value resilient to extreme values. Prior knowledge of ordering numbers and calculating averages will aid your learning.

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Key points

This formula calculates the range $R$ to measure the spread of a dataset. Subtracting the minimum value $x_{\min}$ from the maximum value $x_{\max}$ shows how widely the data is distributed.

R = x_{\max} - x_{\min}

This formula identifies the median $\mathrm{Me}$ when the sample size $n$ is odd. After sorting values in ascending order, the value at position $\frac{n+1}{2}$ is the median.

\mathrm{Me} = x_{\frac{n+1}{2}}

This formula calculates the median $\mathrm{Me}$ when the sample size $n$ is even. After sorting in ascending order, take the average of the two middle values (at positions $\frac{n}{2}$ and $\frac{n}{2} + 1$ ).

\mathrm{Me} = \frac{x_{\frac{n}{2}} + x_{\frac{n}{2}+1}}{2}

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Practice 1Coming soon