You will need

- Knowledge of the lengths of the sides of the triangle.

Instruction

1

To calculate the length of the median formula is applied (see Fig. 1), where:

mc is the length of the median;

a, b, c be the sidelengths of a triangle.

mc is the length of the median;

a, b, c be the sidelengths of a triangle.

# Advice 2: How to find the median of numbers

In statistics for research information along with an average arithmetic indicator of the use and such characteristics as the median. The median is the value of the attribute that divides the number line into two equal parts. And half of numbers up to the median should be no more than its value, and the second half – not less. While median determines the location of the Central numbers in a given row.

Instruction

1

Record given numeric sequence. Follow her ascending. In the set from left to right the numbers must be from smallest to largest.

2

If the number contains an odd number of numbers, the median should take the value exactly in the middle of the set. For example, a numeric sequence: 400 250 640 700 900 100 300 170 550. In this set the numbers are not in order. After sort in ascending order so we get the following number: 100 170 250 300 400 550 640 700 900. As can be seen, the sequence consists of 9 values. The median of the numerical set in this case will be number 400. From his position on one side all numbers are more median, and on the other – not less.

3

When considering the values of the even-numbered sequence, the Central will be not one but two numbers: m and k. Find these numbers also after arranging the set in ascending order. The median of this case will be the average of the data rate values. Calculate it by the formula (m + k)/2. For example, in the sorted series 200 400 600 4000 30000 50000 number 600 and 4000 occupy a Central position. Therefore, the median of a numerical sequence will be the following value: (600 + 4000)/2 = 2300.

4

If the value set contains a large amount of data manually is rather difficult to sort and determine the center of the range. Using a small program you can easily find the median of a sequence of numbers of any dimension. Example code in Pascal:

var M_ss: array[1..200] of integer;

med: real;

k, i, j: integer;

begin

(*Sort the numbers in ascending order*)

for j:=1 to 200-1 do

for i:=1 to 200-j do

begin

if M_ss[i] > M_ss[i+1] then

k:=M[i];

M_ss[i]:=M_ss[i+1];

M_ss[i+1]=k;

end;

(*Finding the median*)

if (length(M_ss) mod 2)=0 then

med:=( M_ss[trunc(length(M_ss))] + M_ss[trunc(length(M_ss))+1])/2

else

med:=M_ss[trunc(length(M_ss))];

end.

Med in a variable contains the median value of the specified numeric array M_ss.

var M_ss: array[1..200] of integer;

med: real;

k, i, j: integer;

begin

(*Sort the numbers in ascending order*)

for j:=1 to 200-1 do

for i:=1 to 200-j do

begin

if M_ss[i] > M_ss[i+1] then

k:=M[i];

M_ss[i]:=M_ss[i+1];

M_ss[i+1]=k;

end;

(*Finding the median*)

if (length(M_ss) mod 2)=0 then

med:=( M_ss[trunc(length(M_ss))] + M_ss[trunc(length(M_ss))+1])/2

else

med:=M_ss[trunc(length(M_ss))];

end.

Med in a variable contains the median value of the specified numeric array M_ss.

Note

The medians of a triangle have the following properties:

1) any of the three medians divides the original triangle into two equal size triangle;

2) All medians of a triangle have a common intersection point. This point is called the center of the triangle;

3) the Medians of a triangle divide it into 6 equal triangles. Equal are called geometric shapes with equal areas.

1) any of the three medians divides the original triangle into two equal size triangle;

2) All medians of a triangle have a common intersection point. This point is called the center of the triangle;

3) the Medians of a triangle divide it into 6 equal triangles. Equal are called geometric shapes with equal areas.

Useful advice

If the triangle is an isosceles triangle, its medians are equal. In addition, in such a triangle the medians coincide with the bisectors and heights.

The angle bisector is the ray that emanates from any vertex of a triangle and forming it divides the angle in half.

Under the height of a triangle is meant the segment, which is drawn from the vertex of the triangle perpendicular to the opposite side.

The angle bisector is the ray that emanates from any vertex of a triangle and forming it divides the angle in half.

Under the height of a triangle is meant the segment, which is drawn from the vertex of the triangle perpendicular to the opposite side.