What is Mean, median, range? — Mathematics

Definition 71.1 Primary & Middle School Mathematics · Chapter 71 — Statistics and Probability

For a series of $N$ numbers:

the mean is the sum of all the values divided by $N$ ;
the median is a value splitting the sorted series in two halves of equal size: for $N$ odd, the middle value; for $N$ even, the midpoint of the two middle values;
the range is the largest value minus the smallest.

Examples

Example 71.2

Marks of a student: $8,\ 12,\ 9,\ 15,\ 11$ .

Mean: $\dfrac{8 + 12 + 9 + 15 + 11}{5} = \dfrac{55}{5} = 11$ .
Median: sort the series: $8, 9, 11, 12, 15$ ; the middle (3rd) value is $11$ .
Range: $15 - 8 = 7$ .

With a sixth mark of $17$ : sorted $8, 9, 11, 12, 15, 17$ , the median becomes the midpoint of $11$ and $12$ , that is $11.5$ , and the mean becomes $\frac{72}{6} = 12$ .

Example 71.3 (Weighted mean)

The shoe sizes sold in a day:

size	$38$	$39$	$40$	$41$	$42$
count	$3$	$7$	$6$	$3$	$1$

The mean size is

\frac{3 \times 38 + 7 \times 39 + 6 \times 40 + 3 \times 41 + 1 \times 42} {3 + 7 + 6 + 3 + 1} = \frac{114 + 273 + 240 + 123 + 42}{20} = \frac{792}{20} = 39.6 .

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Examples

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