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 : 

Where is the balance point for this data ?

Solution :

Example 2 : 

Where is the balance point for this data ?

Solution :

Example 3 : 

Where is the balance point for this data ?

Solution :

Solved Problems

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 two spaces away from the mean and 4 is five 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 two spaces away from the mean.

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

Step 3 :

Now, Just pick a point on the right side which is five 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 one space away from the mean and 8 is three 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 number 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 three spaces away from the mean.

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

Step 3 :

Now, Just pick a point on the left side which is one 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 three spaces away from the mean.

Total on the right side is three spaces.

Step 2 :

On the left side also we should have the same number 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 two spaces away from the mean.

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

Step 3 :

Now, Just pick a point on the left side which is one 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 five spaces away from the mean and 13 is one 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 number 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 four spaces away from the mean.

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

Step 3 :

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

Therefore, the fourth point should be plotted at 16.

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

If you have any feedback about our math content, please mail us : 

v4formath@gmail.com

We always appreciate your feedback. 

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

WORD PROBLEMS

HCF and LCM  word problems

Word problems on simple equations 

Word problems on linear equations 

Word problems on quadratic equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation 

Word problems on unit price

Word problems on unit rate 

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

Double facts word problems

Trigonometry word problems

Percentage word problems 

Profit and loss word problems 

Markup and markdown word problems 

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

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 

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

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

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

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6