Some Important Point Regarding Statistics - Practice Questions & MCQ

Some Important Points Regarding Statistics

1. The sum of the deviation of an observation from their mean is equal to zero. i.e. .
2. The sum of the square of the deviation from the mean is minimum, i.e. 
3. The mean is affected accordingly if the observations are given a mathematical treatment i.e. addition, subtraction multiplication by a constant term.
4. If set of n₁ observations has mean  and a set of n₂ observations has mean , then their combined mean is
5. If set of  n₁ observations has mean  and set of n₂ observations has mean  then their combined variance is given by

          where,  

           are the means and   are the standard deviations of two series.

6. Z-Score Formula: It is a method to compare test results from a normal distribution.

For a random variable (x) from a normal distribution with mean  and standard deviation , the Z-score can be determined by subtracting the mean from x and then dividing by the standard deviation.

Where x is a test value

 is the mean and 

 is the standard deviation (SD).

For the average of a sample of size (n) from a population, the standard deviation is  and the mean is .

Relation between Mean, Mode and Median 

If the distribution is symmetric, the value of mean, mode and median coincide. In symmetric distribution, frequencies are symmetrically distributed on the both side of the center point of the frequency curve.

Distribution which are not symmetric is called a skewed-distribution.

The empirical relation between mean, mode and median in such distributions is: