Page 50 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_ENGLISH

Statistical Methods in Economics

Notes
(60 40 ) + 40X 2
38 =
100

3800 = 2400 + 40X 2

40X 2 = 1400

1400
∴ X 2 = 40 = 35
Hence the wage of the remaining 40 workers in the second shift is Rs. 35.
If we have to find out the combined mean of the three series, the above formula can be
extended as follows:

1 1 + NX 2 2 + N X N X 3
3
X 123 = + N + N N
1 2 3
Median
Median is one of the measures of central tendency. It is a positional average.

Definition of Median
Median may be defined as ‘the middlemost or central value of the series when the values are arranged
in ascending or descending order of magnitude’.
If there is an odd number of an item, then the median is found out by taking the middle most items
of the series only after arranging the data in order of magnitude.
For example, if daily wages of 7 workers are Rs. 127, Rs. 167, Rs. 154, Rs. 177, Rs. 135, Rs. 160 and Rs.
157 and we wish to know the median wage, the wages must be arranged either in ascending order or
descending order of magnitude and the 4 reading will be the median wage.
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Arranged in order of magnitude, the wages might be
Rs. 127 135 154 157 160 168 177
and the median wage is Rs. 157, i.e. the 4 item.
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If there is an even number of items, then the median is half-way between the two middle ones and it
is found by taking the average of these two items. For example, if the marks secured by 10 students
in an examination are 75, 48, 63, 89, 100, 55, 35, 28, 93 and 79 and we wish to know the median mark,
the marks must be arranged either in ascending or descending order of magnitude and then the
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average of the value of the 5 item and the 6 item will be the median mark.
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Arranged in order of magnitude, the marks might be 28, 35, 48, 55, 63, 75, 79, 89, 93, 100 and the
63 + 75 138
median marks is Rs. = = 69, i.e. the average of the 5 item and the 6 item.
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2 2
Properties of Median
Median is of the following properties:
1. Median may be the middlemost value of the series when the values are arranged in order of
magnitude.
2. Median is influenced by the position of items in the array but not by the size of the items.
3. The value of the median of a series may or may not coincide with the value of an existing item.
4. The median cannot readily be located unless the data have been put into an array or into a
frequency distribution.

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