Simple..let the terms.=X
then.. increase mean ..
=. 5x/x. = 5 ...
so increased by 5

Explanation:

To understand why the mean is increased by 5 when each observation of the data is increased by 5, let's consider the definition of the mean and how it is calculated.

Mean:
The mean is a measure of central tendency that represents the average value of a set of observations. It is calculated by summing up all the observations and dividing the sum by the total number of observations.

Effect of Increasing each Observation by 5:
When each observation is increased by 5, it means that every value in the data set is increased by the same amount. This will result in a shift of the entire data set to the right. Since the mean takes into account all the values in the data set, increasing each observation by 5 will increase the sum of the observations.

Effect on the Mean:
As the sum of the observations is increased, the denominator (total number of observations) remains the same. Therefore, the mean is calculated by dividing a larger sum by the same number of observations. This will result in a larger mean value.

Example:
Let's consider a simple example to illustrate this concept. Suppose we have the following data set with 3 observations: 2, 4, 6.

The original mean is calculated as:
Mean = (2 + 4 + 6) / 3 = 4

If we increase each observation by 5, the new data set becomes: 7, 9, 11.

The new mean is calculated as:
Mean = (7 + 9 + 11) / 3 = 9

Comparing the original mean (4) with the new mean (9), we can see that the mean has increased by 5 when each observation was increased by 5.

Conclusion:
In conclusion, when each observation of the data is increased by 5, the mean is increased by 5. This is because increasing each observation increases the sum of the observations, resulting in a larger mean value.