A village consists of twenty (20) households with the following annual incomes-
(Incomes $00) 30 20 50 40 60 40 40 50 20 60 80 40 20 20 70 40 70 30 40 80
(a) Determine the (i) mean income: [4 marks] (ii) modal income; [ 2 marks] (iii) median income. [2 marks]
(b) What is the range of income distribution? [2 marks]
(c) Calculate the total tax that could be generated from the village if (i) a flat rate tax of 7% is imposed on all households; [5 marks] (ii) a flat rate tax of 15% is imposed on all households earning $4,000 per annum and above. [5 marks]
Explanation
(a) (i) \(\frac{30 + 20 + 50 + 40 + 60 + 40 + 40 + 50 + 20 + 60 + 80 + 40 + 20 + 20 + 70 + 40 + 70 + 30 + 40 + 80}{20}\) = \(\frac{900}{20}\) = 45
Mean income = $4,500
(ii) Modal income = $4,000
(iii) Median Income 20,20,20,20,30,30,40,40,40,40,40,40,50,50,60,60,70.70.80.80
Using middle values = \(\frac{40+40}{2}\) = \(\frac{80}{2}\) Median income = $4,000
(b) Range = $8,000 - $2,000 = $6,000
(c) (i) $90,000 x \(\frac{70}{100}\) = $6,300
(ii) 40+40+40+40+40+40+50+50+60+60+70+70+80+80 = 760
= $76000 x \(\frac{15}{100}\) = $11,400.