UGANDA MANAGEMENT INSTITUTE

DPAM 2014/2015

Philip Odida: 14/DPAM/000/KLA/EVE/0040

Module: Quantitative Methods in Decision Making

Module lecturer:Kimbugwe Hassan, Consultant,

Uganda Management Institute

Individual Coursework:7th November, 2014

The following data represents the monthly income (Shs 000) of 80 randomly selected villagers after a poverty reduction exercise had been carried out in Goma sub-county. Before the exercise, those in charge of the poverty reduction program had carried out a baseline survey and established that, on average, the monthly income was Shs 26,500 per month.

Table 1.Sample data collected from Goma sub-county.2223101739543347

1633241047314222

4023382925372212

1514242252134827

2729244528452144

4923162423232913

2234312922431532

1721212435371936

2520213941443923

1424213823285337

i)

ii)Frequency distribution table for randomly selected villagers in Goma sub-county.ClassTallyFXfxfx2cf

10 19IIII IIII IIII1414.52032,943.514

20 29IIII IIII IIII IIII IIII IIII IIII3524.5857.521,008.7249

30 39IIII IIII IIII I1634.555219,04465

40 49IIII IIII II1244.553423,76377

50 - 59III355.5166.59,240.7580

80173.52,31376,000

iii)

The Mean of the sample (x) is derived from the following equation: fx/N where fx = 2,313 and N = 80x = 2,313/80 = 28.91

The Median of the sample (Md) is derived from the following equation:L+[N/2 - cfb/fc]c

where L = 20-0.5 = 19.5; N = 80; cfb = 14; fc = 35 and

c = 29.5 19.5 = 10Solution:Md = 19.5 + [80/2 14/35]10

= 19.5 + [40-14/35]10

= 19.5 + [26/35]10

= 19.5 + 7.43 = 26.928

Md = 26.93

The Mode of the frequency distribution is derived from the following equation:

Mo = L+[d1/d1 + d2]cWhere L = 19.5; d1 = 35-14 = 21; d2 = 35-16 = 19 and c = 10

Solution: Mo = 19.5 + [21/21+19]10

= 19.5+[21/40]10

= 19.5+[0.525]10

= 19.5+5.25 = 24.75

Mo = 24.75

The mean, median and mode of the frequency distribution is 28.91, 26.93, 24.75 respectively. The median of the class calculated in the above exercise (26.93), is closest to the result of the baseline survey that established that on average, the monthly income of the 80 randomly selected villagers in Goma sub-county was 26,500 shillings.

The median computed here is the most appropriate average of the frequency distribution because the median value is not affected by extreme values. The highest monthly income in the sample, for instance is 54,000 shillings, while the lowest monthly income is 10,000 shillings.iv)

The data obtained in the random sample above pertain to the measures of central tendency, which are useful for public administration and management in the sense that they serve as a basis for analysis in a manner that can contribute to scientifically informed decision making. In management terms, the data serves essentially as a basis for planning, decision making with a view to reasonable resource allocation. v)

-The standard deviation () of the frequency distribution above is derived from the following equation: = fx2/fx-(X)2 where fx2 = 76,000; fx = 2,313 and X = 28.91= 76,000/2,313-(28.91)2= 32.86-835.79

=-802.93

= 28.34

The Coefficient of variation of the incomes in the frequency distribution is derived from the following equation:

/X= 28.34/28.91 = 0.98The coefficient of variation is = 98%

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