This document discusses key statistical concepts related to measures of central tendency (mean, median, mode), measures of variation (variance, standard deviation), and distribution shape. It provides formulas to calculate variance, standard deviation, and coefficient of variation. The relationships between mean, median and mode depend on whether a distribution is symmetrical, positively skewed, or negatively skewed. Mode is equal to 3 times the median minus 2 times the mean according to Karl Pearson's formula.

1. Relation Between
Mean, Median & Mode
21COM2T412: Business Statistics
Dr. Neerupa Chauhan
Asst. Professor
Kristu Jayanti College, Autonomous
(Reaccredited A++ Grade by NAAC with CGPA 3.78/4)
Bengaluru – 560077, India

2.  In symmetrical distributions,
the median and mean are
equal
For normal distributions,
mean = median = mode
 In positively skewed
distributions, the mean is
greater than the median
In negatively skewed
distributions, the mean is
smaller than the median
Relation Between
Mean, Median & Mode

3. Empirical Relationship
Relation between Mean, Median, and Mode is that Mode is equal to
the difference between 3 times median and 2 times mean. It is
expressed using Karl Pearson's formula.

5. •Important Measure of Variation
•Shows Variation About the Mean:
•For the Population:
•For the Sample:
Variance
 
N
Xi
 

2
2


 
1
2
2




n
x
x
s
i
For the Population: use N in the
denominator.
For the Sample : use n - 1 in
the denominator.

6. •Important Measure of Variation
•Shows Variation About the Mean:
•For the Population:
•For the Sample:
Standard Deviation
 
N
Xi
 

2


 
1
2




n
x
x
s
i

7. Coefficient of Variation
•Measure of Relative Variation
•Always a %
•Shows Variation Relative to Mean
•Used to Compare 2 or More Groups
•Formula (for Sample):
100%








X
SD
CV

8. Shape of Curve
 Describes How Data Are Distributed
 Measures of Shape:
 Symmetric or skewed
Right-Skewed
Left-Skewed Symmetric
Mean = Median = Mode
Mean Median Mode Median Mean
Mode

9. • Thank you