The ogives shown are based on U.S. Census data and show the average annual perso
ID: 2946849 • Letter: T
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 dollars.
(a) How were the percentages shown in graph (ii) computed?
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 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 multiplying 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 dividing each of the cumulative frequencies in graph (i) by 50 and then converting those values into percents.
(b) How many states have average per capita income less than 37.5 thousand dollars?
(c) How many states have average per capita income between 42.5 and 52.5 thousand dollars?
(d) What percentage of the states have average per capita income more than 47.5 thousand dollars?
%
Explanation / Answer
(a)
(17/50)x100=34%, (35/50)x100=70%, (45/50)x100=90%, (49/50)x100=98%, (50/50)x100=100%
Hence 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.
(b) Draw a perpendicular line from x=37.5 in upward direction and then draw a line fparallel to x axis from the intersect point of ogive and vertical line, then we find that the line cuts the y axis at 35. So total no. of states have average per capita income less than 37.5 thousand dollars is 35.
(c) Using same procedure mentioned in (b), total no. of states have average per capita income less than 42.5 thousand dollars is 45
and total no. of states have average per capita income less than 52.5 thousand dollars is 50.
Hence total no. of states have average per capita income between 42.5 and 52.5 thousand dollars=50-45=5
(d) The percentage of the states have average per capita income more than 47.5 thousand dollars=100-98=2%