Statistics for management

ALLAMA IQBAL Open University
Islamabad




Statics for management (5412)


SUBMITTED BY: Ahmed Hussain Shah
STUDENT I’D : 0000512568


SEMESTER: Spring ,2024
ASSIGNMENT NO. 2

SUBMITTED TO: RESPECTED
MAM SOBIA TABASSUM

,QUESTION NO.1
(a) What do you understand by coefficient of correlation?
How will you determine Aral Pearson’s coefficient of
correlation?
ANSWER;


Coefficient of Correlation:


The coefficient of correlation measures the strength
and direction of the linear relationship between two
continuous variables, X and Y. It ranges from -1 to 1,
where:


- 1: Perfect positive correlation
- -1: Perfect negative correlation
- 0: No correlation

, Karl Pearson's Coefficient of Correlation (r):


Karl Pearson's coefficient of correlation, also known
as Pearson's r, measures the linear relationship
between two variables.


Formula:


r = Σ[(xi - x̄)(yi - ȳ)] / sqrt[Σ(xi - x̄)² * Σ(yi - ȳ)²]


where:


- xi and yi are individual data points
- x̄ and ȳ are means of X and Y variables
- Σ denotes summation
- n is the sample size

,  Steps to calculate Pearson's r:


1. Calculate the mean (x̄ and ȳ) of both variables.
2. Calculate deviations from the mean for each data point (xi - x̄
and yi - ȳ).
3. Calculate the product of deviations for each pair [(xi - x̄)(yi -
ȳ)].
4. Sum the products (Σ).
5. Calculate the sum of squared deviations for X and Y [Σ(xi - x̄)²
and Σ(yi - ȳ)²].
6. Take the square root of the product of sums from step 5.
7. Divide the sum from step 4 by the result from step 6.