Question

The ogives shown are based on U.S. Census data and show the average annual personal income per capita for each of the 50 states. The data are rounded to the nearest thousand dol lars. (i) Ogive Personal Income per Capita by State Cumulative frequency 50 49 50 40 30 20 10 Per capita income 37.5 ($1000) 27.5 32.5 42.5 47,5 52.5 (i) Ogive Showing Cumulative Percentage of Data Personal Income per Capita by State Percent of states 100% 100 90 98% 86% 80 68%. 70 60 50 40 34% 30 20 10 0%. Per capita income ($1000) 27.5 32.5 37.5 42.5 47.5 52.5 (a) How were the percentages shown in graph (ii) computed? 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 fractions. 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 percents. The percentages in graph (ii) were computed by multiplying each of the cumulative frequencies in graph (i) by 100 and then converting those values into decimals. The percentages in graph (ii) were computed by dividing each of the cumulative frequencies in graph (i) by 100 and then converting those values into decimals. The percentages in graph (ii) were computed by multiplying each of the cumulative frequencies in graph (i) by 50 and then converting those values into percents.

Answer 1

The percentages shown in graph (ii) are computed by dividing each cumulative frequency by 50, since there are 50 data values. Then the values obtained are converted to percentages. The correct option is, option(B). (b) The number of states that have average per capita income less than 37.5 thousand dollars is 34 states. The number of states that have average per capita income between 42.5 and 52.5 thousand dollars is calculated below. per capita b/w 42.5 and 52.5 = states with average 52.5 - states with average 42.5 =50 - 43 Therefore, 7 states have average per capita income between 42.5 and 52.5. (d) The number of states that average per capita income more than 47.5 thousand dollars is 1. The percentage is computed as follows, percent states with per capita more than 47. 5 0 2x100 Total number of states L = 3x100 50 = 2% Therefore 2% of the states have average per capita income more than 47.5 thousand dollars.