Question

Answer the following questions in about 125 words:
(i) Explain relative positions of mean, median and mode in a normal
distribution and skewed distribution with the help of diagrams.
(ii) Comment on the applicability of mean, median and mode (hint: from their
merits and demerits).
(iii) Explain the process of computing Standard Deviation with the help of an
imaginary example.
(iv) Which measure of dispersion is the most unstable statistic and why?
(v) Write a detailed note on the degree of correlation.
(vi) What are various steps for the calculation of rank order correlation?

Answer 1

     Degree of correlation

Correlation is a method which determines the relationship of one variable with the other. The coefficient of correlation is denote by r or p(rho).  Positive, Negative, Zero, Linear or Curvilinear(Non-Linear) correlation are the types of correlation.

Positive Correlation:-

When increase in one variable(X) is followed by increase in other variable(Y) is positive correlation.

Negative Correlation:-

When increase in one variable(X) results in a corresponding decrease in other variable(Y) is negative correlation.

Zero Correlation:-

When no relationship between two variables is known as zero correlation.

Linear Correlation:-

When the ratio of change between the two variables either in the same direction or opposite direction and the graphical representation of the one variable with respect to other variable is straight line.  

Solution 2:  

Various steps for the calculation of Rank order of correlation

Spearman Rank Correlation when there is no Tied Ranks:-

$\rho =1-\frac{(\Sigma6 d_i^2 )}{(n(n^2-1)}$

Step-1:

Find the ranks for each individual subject. Order the scores from greatest to smallest, allot the rank 1 to the highest score, 2 to the next highest score and so on.

A Score   Rank B Score  Rank

22             3               5          5

33             2                38    1

20             5                12    4

44             1               23    3

21             4               36    2

Step-2:

Add a third column d in your data. The d is difference between ranks.

A Score   Rank B Score Rank d

22              3             5            5        2

33             2             38     1        1

20             5             12     4        1

44             1             23     3        2

21            4             36     2        2

Step-3:  

Add 4th column in your data i.e. $d^2$ and then square your d values.

A Score Rank B Score Rank d d²

22             3              5                5 2 4

33             2             38        1 1 1

20              5              12       4 1 1

44              1              23       3 2 4

21              4             36       2 2 4

Step-4:

Sum of $d^2$ values i.e. ∑$d^2$ .

4+1+1+4+4=14

Step-5:

Insert the values into the given formula.

Spearman Rank Correlation when there is Tied Ranks:-

Tied ranks are those ranks where two items in a column have same rank. For example, two scores are tied at 3 and 4. Then the mean rank will be 3.5