Let's assume there are 3 people in Room A and another 3 people in Room B. The ages of the people in Room A are 25, 25, and 25. The ages of the people in Room B are: 10, 25, and 40. The mean of the ages in both rooms is 25. Does that mean that both room have populations that are equivalent? Is it fair to say that the number 25 is truly an indication of how old the people in the two rooms are? Well, not exactly... There is NO dispersion in the ages of the people in Room A (since everybody is the same age...), but there is large dispersion in Room B.

Question

Let's assume there are 3 people in Room A and another 3 people in Room B.  The ages of the people in Room A are 25, 25, and 25.  The ages of the people in Room B are: 10, 25, and 40.   The mean of the ages in both rooms is 25.  Does that mean that both room have populations that are equivalent?  Is it fair to say that the number 25 is truly an indication of how old the people in the two rooms are?  Well, not exactly...  There is NO dispersion in the ages of the people in Room A (since everybody is the same age...), but there is large dispersion in Room B.

The standard deviation of the ages in Room A is zero; the standard deviation of the ages in Room B is 12.25. So, when we say that for Room B the mean is 25 and the standard deviation is 12.25, we get a better picture of the age distribution in the room. Standard deviation is a measure of the "spread" in the data.

Also, how did I get 12.25? How was it calculated?

Also, how did I get 12.25?  How was it calculated?

Mahendra · Answer

Standard Deviation = SQRT [ {sqr(10-25) + sqr (25-25) + sqr (40-25)}/3 ]