Question

Table #2.2.10: Data of Median Income for Females

$31,862	$40,550	$36,048	$30,752	$41,817	$40,236	$47,476	$40,500
$60,332	$33,823	$35,438	$37,242	$31,238	$39,150	$34,023	$33,745
$33,269	$32,684	$31,844	$34,599	$48,748	$46,185	$36,931	$40,416
$29,548	$33,865	$31,067	$33,424	$35,484	$41,021	$47,155	$32,316
$42,113	$33,459	$32,462	$35,746	$31,274	$36,027	$37,089	$22,117
$41,412	$31,330	$31,329	$33,184	$35,301	$32,843	$38,177	$40,969
$40,993	$29,688	$35,890	$34,381

The median incomes of females in each state of the United States, including the District of Columbia and Puerto Rico, are given in table #2.2.10 ("Median income of," 2013). Create an ogive for the data in table #2.2.10. Describe any findings you can from the graph.

Answer 1

Class Interval	Frequency	Upper Limit	Less than cumulative frequency
22000    -    27500	1	Less than 27500	1
27500    -    33000	14	Less than 33000	15
33000    -    38500	21	Less than 38500	36
38500    -    44000	11	Less than 44000	47
44000    -    49500	4	Less than 49500	51
49500    -    55000	0	Less than 55000	51
55000    -    60500	1	Less than 60500	52

Class interval can be calculate as follows

Minimum Value	22117
Maximum Value	60332
Range	38215

Let us consider we need 7 classes (classes can be taken in a range of 5 - 15)

So, class width = Range/ 7 = 38125/7 = 5459.285 5500

lower value is 22117, so consider the lower class as 22000 and upper class = 27500

So the difference bewtween lower and upper class = 275050 - 22000 = 5500

Similarly, calculate the rest classes

Cumulative frequency can be calculate by adding up the frequency with the next frequency

We can calculate Medina from Ogive curve, we have N = 52

So the middle value is half of 52 = 26

Frequencys are plotted on vertical ( Y-axis)

Draw line originate from Y-axis to ogive curve and then from the ogive curve draw perpendicular line on x axis.

The value of x axis will the median value.

Once you graph the ogive curve on graph paper, you will get the exact value for median.

Similarly,

Can calculate 1^st and 3^rd Quartile

1^st Quartile = (N+1) / 4 = (52 + 1)/4 = 13.25

2^nd Quartile = 3(N+1) / 4 = 39.75