(a) Ngee Ann Polytechnic (MP) is reviewing their nancial aid policies, aimed at easing the financial strain on low income families. A survey was conducted and monthly per capita income from 25 low income families was taken and it was found that the mean income was $550 with a standard deviation of $50. The median was $500, the highest value was $690 and the range was $340. There is no mode. (i) It was discovered that all 25 recorded income were recorded wrongly and should have been $15 more for each family. Find the new mean, median and standard deviation. (ii) To understand the distribution of family income better, NP projected that high income families with have much higher per capita income. They estimated that high income families will have per capita income 5 times more than the louncome families. NP decided to use the mg per capita income (use the sample income from part (a)(i)) from the low income families and multiply by 5 to be the sample per capita income for the high income families. Find the new mean, median and variance of these projected m families. (b) A sample of 80 low income families were sampled and their monthly average per capita expenditure was also recorded. Per Capita Income (5) No. of graduates Per Capita Expenditure ($) 0 up to 100 9 64 100 up to 200 13 125 200 up to 300 9 180 300 up to 400 8 338 400 up to 500 18 280 500 up to 600 19 419 600 up to 700 4 526 Table 1.1 Based on the 80 samples, (i) By performing appropriate calculations and showing all workings, determine the skewness ofthe distribution of monthly per capita income. (ii) What is the standard deviation of the monthly per capita income? (iii) A lecturer was tasked to find the relationship between per capita income and per capita expenditure. Ignoring the number of graduates, use the data in Table 1.1 with the midpoint of Per Capita Income as the dependent variable and Per Capita Expenditure as the independent variable, determine the least square regression line. (iv) Determine the correlation coefcient