Question

Personal Income per Capita by State Cumulative frequency 50 40 за 20 10 48 15 34 15 Per capita income $1000) 27.5 32.5 375 42.5 475 52.5 (i) Ogive Showing Cumulative Percentage of Data Personal Income per Capita by State Percent of states 100% 100 90 80 70 60 50 40 30 20 10 96 30 Per capita income (S1000) 27.5 325 37.542.5 475 52.5 (a) How were the percentages shown in graph (i) computed? 0 The percentages in graph (ii) were computed by dividing each of the cumulative frequencies in graph ( by so and then on erting those vales into fractions O The percentages in graph (u) were computed by multiplying each of the curmulative frequencies in graph (0) by 100 and then converting those values into decimals. O The percentages in graph (i) were computed by dividing each of the cumulative frequencies Iin graph (O) by S0 and then converting those values into percents. O The percentages in graph (i) were computed by dividing each of the cumulative frequencies in graph (0) by 100 and then converting those values into decimals. O The percentages in graph () were computed by multiplying each of the cumulative frequencies in graph () by 50 and then converting those values into percents.

Answer 1

a) The percentages in graph (ii) were computed by dividing each of the cumulative frequencies in graph(i) by 50 and then converting those values into decimals.

eg. for cumulative frequency 15 , the cumulative percentage = $\dpi{80} \fn_jvn \frac{15}{50} \times 100$ % = 30 %

b) From the graph (i) the value corresponding 37.5 in y- axis is 34, hence 34 states have average per capita income of 37.5$ or less.

c)  From the graph (i) the value corresponding 42.5 in y- axis is 45 and the value corresponding 52.5 in y- axis is 50, hence 50 - 45 = 5  states have average per capita income between 42.5$ and 52.5 $.

d) From the graph (ii) the value corresponding 47.5 in y- axis is 96%,  hence 100 - 96 = 4% state have average per capita income more than 47.5.