Page 149 - DMGT404 RESEARCH_METHODOLOGY

Unit 8: Descriptive Statistics

 w X 32500.2 Notes
X for College A  A A 
w  w A 480 = 67.71%
 w X 59999.2
X for College B  B B 
w  w B 800 = 75%
Since the weighted average of pass percentage is higher for college B, hence college B is better.

Notes If X denotes simple mean and X denotes the weighted mean of the same data, then
w
1. X  X , when equal weights are assigned to all the items.
w
2. X  X , when items of small magnitude are assigned greater weights and items of
w
large magnitude are assigned lesser weights.
3. X  X , when items of small magnitude are assigned lesser weights and items of
w
large magnitude are assigned greater weights.

Task Analyse the properties of Arithmetic Mean.

8.2.3 Median

Median of distribution is that value of the variate which divides it into two equal parts. In terms
of frequency curve, the ordinate drawn at median divides the area under the curve into two
equal parts. Median is a positional average because its value depends upon the position of an
item and not on its magnitude.

Median can be determined under various situations like:
When Individual Observations are Given
The following steps are involved in the determination of median:
1. The given observations are arranged in either ascending or descending order of magnitude.
2. Given that there are n observations, the median is given by:

 n  1
(a) The size of   th observations, when n is odd.
 2 
n  n 
(b) The mean of the sizes of th and    1  th observations, when n is even.

2 2
Example: Find median of the following observations:
20, 15, 25, 28, 18, 16, 30.

Solution:

Writing the observations in ascending order, we get 15, 16, 18, 20, 25, 28, 30.

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