**Mean as a Balance Point : **

Mean can be defined as a balance point on a number line where the data distribution is balanced.

This means that the sum of the distances from the mean of all the points above the mean is equal to the sum of the distances of all the data points below the mean.

**In more detail :**

Th quantity on each side of mean (balance point) on a number line will be equal.

**Example 1 : **

**Example 2 : **

**Example 3 :**

**Problem 1 :**

A set of data has four values. Three of the values are plotted on the number line below.

Where should the fourth point be plotted so the mean of the data set is 9 ?

**Solution : **

**Step 1 :**

Let us consider on the left side of the mean "9". Two points are marked on the number line. They are 7 and 4.

"7" is 2 spaces away from the mean and "4" is 5 spaces away from the mean.

Total on the left side is

= 2 spaces + 5 spaces

= 7 spaces

**Step 2 :**

On the right side also we should have the same no. of spaces if the mean is "9".

Already there is a point on the right side of the mean, that is "11". And "11" is 2 spaces away from the mean.

So we need 5 more spaces on the right side in order to have the total of 7 spaces.

**Step 3 :**

Now, Just pick a point on the right side which is 5 spaces away from the mean "9". That is "14".

Therefore, the fourth point should be plotted at 14.

**Problem 2 :**

A set of data has four values. Three of the values are plotted on the number line below.

Where should the fourth point be plotted so the mean of the data set is 5 ?

**Solution : **

**Step 1 :**

Let us consider on the right side of the mean "5". Two points are marked on the number line. They are 6 and 8.

"6" is 1 space away from the mean and "8" is 3 spaces away from the mean.

Total on the right side is

= 1 space + 3 spaces

=** **4 spaces

**Step 2 :**

On the left side also we should have the same no. of spaces if the mean is "5".

Already there is a point on the left side of the mean, that is "2". And "2" is 3 spaces away from the mean.

So we need 1 more space on the left side in order to have the total of 4 spaces.

**Step 3 :**

Now, Just pick a point on the left side which is 1 space away from the mean "5". That is "4".

Therefore, the fourth point should be plotted at 4.

**Problem 3 :**

A set of data has 3 values. Two of the values are plotted on the number line below.

Where should the third point be plotted so the mean of the data set is 12 ?

**Solution : **

**Step 1 :**

Let us consider on the right side of the mean "12". Only one point is marked and it is "15".

"15" is 3 spaces away from the mean.

Total on the right side is** **3 spaces.

**Step 2 :**

On the left side also we should have the same no. of spaces if the mean is "12".

Already there is a point on the left side of the mean, that is "10". And "10" is 2 spaces away from the mean.

So we need 1 more space on the left side in order to have the total of 3 spaces.

**Step 3 :**

Now, Just pick a point on the left side which is 1 space away from the mean "12". That is "11".

Therefore, the fourth point should be plotted at 11.

**Problem 4 :**

A set of data has 4 values. Three of the values are plotted on the number line below

Where should the fourth point be plotted so the mean of the data set is 14 ?

**Solution : **

**Step 1 :**

Let us consider on the left side of the mean "14". Two points are marked on the number line. They are 9 and 13.

"9" is 5 spaces away from the mean and "13" is 1 space away from the mean.

Total on the left side is

= 5 spaces + 1 space

=** **6 spaces

**Step 2 :**

On the right side also we should have the same no. of spaces if the mean is "14".

Already there is a point on the right side of the mean, that is "18". And "18" is 4 spaces away from the mean.

So we need 2 more spaces on the right side in order to have the total of 6 spaces.

**Step 3 :**

Now, Just pick a point on the right side which is 2 spaces away from the mean "14". That is "16"

Therefore, the fourth point should be plotted at 16.

After having gone through the stuff given above, we hope that the students would have understood the stuff mean as a balance point.

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

Widget is loading comments...

You can also visit our following web pages on different stuff in math.

**WORD PROBLEMS**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**