**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.

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