Page 102 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_ENGLISH

Statistical Methods in Economics

Notes Example 4: Calculate mean deviation from the following data:

Class-interval Frequency Class-interval Frequency
10–30 6 90–110 21
30–50 53 110–130 26
50–70 85 130–150 4
70–90 56 150–170 4

Given that the median of the above data is 60.5.
Solution:

d
Class-interval f Mid-points Deviation M fd M
10–30 6 20 |40.5| 243.0
30–50 53 40 |20.5| 1086.5
50–70 85 60 |0.5| 42.5
70–90 56 80 |17.5| 1092.0
90–110 21 100 |39.5| 2139.5
110–130 26 120 |59.5| 1547.0
130–150 4 140 |79.5| 318.0
150–170 4 160 |99.5| 398.0

∑ fd M = 6,866.5

∑ fd
δ M = N M , ∑ fd M = 6,866.5, N = 255

6,866.5
∴ δ M = 255 = 26.93.

Example 5: Calculate mean deviation from mean from the following data:
X 0–100 100–200 200–300 300–400 400–500 500–600 600–700

f 6 5 8 15 7 6 3
Solution:

d
X f Mid (M) values Deviation from ( ) fd X
X
X
0–100 6 50 |284| 1,704
100–200 5 150 |184| 920
200–300 8 250 |84| 672
300–400 15 350 |16| 240
400–500 7 450 |116| 812
500–600 6 550 |216| 1,296
600–700 3 650 |316| 948
∑ f = 50 ∑ fx = 6,592
X

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