Question

(A) If there is high variability in the distribution of income and wealth of the country then which value is compromised?

(B) Mean and standard deviation of two distributions of 100 and 150 items are 50, 5 and 40, 6 respectively. Find the standard deviation of all the 250 items taken together.

Answer 1

(A) The high variability in the distribution of income and wealth shows that there are many people who are living at a very low income while there are few people who have amassed huge wealth and taking advantage of luxuries of life. In this case, the value of equity is compromised in the society as high level of disparity of income and wealth makes it prone to social unrest.

(B)

$\text{Combined Mean}=\frac{N_1\overline{X_1}+N_2\overline{X_2}}{N_1+N_2}=\frac{100\times 50+150\times 40}{100+150}=\frac{11000}{250}=44\text{Calculation of combined standard deviation}{\sigma }_{1,2}=\sqrt{\frac{N_1{\sigma }_1^2+N_2{\sigma }_2^2+N_1{d}_1^2+N_1{d}_2^2}{N_2+N_2}}{d}_1=\overline{X_1}-{\overline{X}}_{1,2}\text{and}{d}_2=\overline{X_2}-{\overline{X}}_{1,2}{d}_1=50-44=6\text{and}{d}_2=40-44=-4{\sigma }_{1,2}=\sqrt{\frac{100(5{)}^2+150(6{)}^2+100(6{)}^2+150(-4)}{100+150}}{\sigma }_{1,2}=\sqrt{\frac{2500+5400+3600+2400}{100+150}}=\sqrt{55.6}=7.456$