Subject : Business Mathematics
Prof. Shruti Chandak
Correlation is the relationship that exists
between two or more variables.
If variables are related to each other in such a
way that change in one creates a
corresponding change in other, then the
variables are said to be correlated.
The relationship between heights and weights.
The relationship between the quantum of rainfall
and yield of crop.
The relationship between the price of commodity
and demand of commodity.
Positive and Negative Correlation
Linear and Non-linear Correlation
Simple, Partial and Multiple Correlation
If r = +1, then perfect Positive Correlation.
If 0<r<+1, then Positive Correlation.
If -1<r<0, then Negative Correlation.
If r = -1, then perfect Negative Correlation.
If r = 0, then no linear Correlation.
Methods of
correlation
Graphic Algebraic
Methods Methods
Scatter Diagram Simple graphic
Method Method
Karl Pearson’s Spearman’s Concurrent
Coefficient of Rank difference Deviation Others
correlation Method method
P1. Calculate the coefficient of correlation for the
following data :--
X 9 8 7 6 5 4 3 2 1
Y 15 16 14 13 11 12 10 8 9
P2. Calculate the Pearson’s coefficient of
correlation for the following data :--
Price (Rs)
22 24 26 28 30 32 34 36 38 40
Demand
(Tons) 60 58 58 50 48 48 48 42 36 32
P3. Calculate the Pearson’s coefficient of
correlation for the following data :--
◦ Sum of deviations of x = 5
◦ Sum of deviations of y = 4
◦ Sum of square of deviations of x = 40
◦ Sum of square of deviations of y = 50
◦ Sum of the product of deviations of x and y = 32
◦ No. of pairs of observations = 10
P4. Calculate the Pearson’s coefficient of
correlation for the following data :--
X 100 110 115 116 120 125 130 135
Y 18 18 17 16 16 15 13 10
P5. Calculate the Pearson’s coefficient of
correlation for the following data :--
Marks in 20 35 15 40 10 35 30 25 45 30
statistics (X)
Marks in 25 30 20 35 20 25 25 35 35 30
Accounts (Y)
P6. Calculate the Pearson’s coefficient of correlation
for the following data :--
X Y
series series
No. of observations 15 15
Arithmetic Mean 25 18
S.D 5 5
Ʃ (X – 25) (Y – 18) = 125
P7. The total of the multiplication of deviation of
X and Y = 3044. No. of pairs of the observation is
10. Total of deviations of X=-170. Total of
deviations of y = -20. Total of the squares of
deviations of x = 8288. Total of the squares of
deviations of y = 2264. Find out the coefficient of
correlation when arbitrary means of x and y are
82 and 68 respectively.
P8. Two teachers were asked to rank 7 students on
the basis of their singing competition. The ranks
given by them are given below :--
Student 1 2 3 4 5 6 7
Teacher 1 4 2 1 3 5 7 6
Teacher 2 1 3 2 4 5 6 7
Calculate the Spearman’s coefficient of correlation.
P9. Two teachers were asked to rank 7 students on
the basis of their singing competition. The marks
assigned to these students out of maximum 50 are
given below :--
Student 1 2 3 4 5 6 7
Teacher 1 39 43 45 42 36 32 28
Teacher 2 46 41 44 40 38 36 32
Calculate the Spearman’s coefficient of correlation.
P10. Calculate the coefficient of rank correlation
from the following data :--
X 48 33 40 9 16 16 65 24 16 57
y 13 13 24 6 15 4 20 9 6 19
P11. Calculate the coefficient of rank correlation
from the following data :--
X 8 10 7 15 3 20 21 5 10 14 8 16 22 19 6
y 3 12 8 13 20 9 14 11 4 16 15 10 18 23 25
P12. The coefficient of rank correlation of the
marks obtained by 10 students in two particular
subjects was found to be 0.5. It was later
discovered that the difference in ranks in two
subjects obtained by one of the student was
wrongly taken as 3 instead of 7. What should be
the correct value of coefficients of rank
correlation?
