Page 100 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_ENGLISH

Statistical Methods in Economics

Notes Answer: The mean deviation from arithmetic mean of the given data is 0.175.
Example 3: Find the mean deviation for the following data (from median and mean)

Items 0 1 2 3 4 5 6 7 8 9 10 11 12
Frequency 15 16 21 10 17 8 4 2 1 2 2 0 2

Solution: To find Median
Items in ascending order Frequency Cumulative Frequency
0 15 15
1 16 31
2 21 52
3 10 62
4 17 79
5 8 87
6 4 91
7 2 93
8 1 94
9 2 96
10 2 98
11 0 98
12 2 100

∑ f = 100
( + )N1
Median = th item = 55.5th item
2
∴ Median = 2.

Deviation from Median

Items f Deviation( M ) fd M
d
0 15 0 – 2 = |2| 2 × 15 = 30
1 16 1 – 2 = |1| 1 × 16 = 16
2 21 2 – 2 = |0| 00
3 10 3 – 2 = |1| 1 × 10 = 10
4 17 4 – 2 = |2| 2 × 17 = 34
5 8 5 – 2 = |3| 3 × 8 = 24
6 4 6 – 2 = |4| 4 × 4 = 16
7 2 7 – 2 = |5| 5 × 2 = 10
8 1 8 – 2 = |6| 6 × 1 = 6
9 2 9 – 2 = |7| 7 × 2 = 14
10 2 10 – 2 = |8| 8 × 2 = 16
11 0 11 – 2 = |9| 9 × 0 = 00
12 2 12 – 2 = |10| 10 × 2 = 20
∑ fd M = 196

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