#2. The following back-to-back stem-and-leaf plot gives the percentage ofresiden
ID: 3052379 • Letter: #
Question
#2. The following back-to-back stem-and-leaf plot gives the percentage ofresidents "65 and over" (right) and those "aged 18 to 24" (left) for each of the fifty states aged 18 to 24 65 and over 17 0 16 14 03478 11 23 33479 15 3.4 3 13 000011233345569 0 12 00001 1333447 89 21 1 8887766543 32221 10010 6 99999998877765522229 578 4778 8 6 So 6 3 (a) For what proportion of states is the percentage of residents 65 and over less than 10%? (b) What is the median percentage of residents aged 18 to 24? (c) For the distribution of percentages of residents 65 and over what is the third quartile? S50+ le.orio.-To.oExplanation / Answer
a) 65 and over less than 10%
0.1* (50+1)= 5.1 th observation
From down to up: 5th observation= 98 and 0.1*(106-98)= 0.8
5.1th observation= 98+0.8= 98.8
b) median= (n+1)/2th observation:
51/2= 25.5th observation=(26+25)/2 th observation = (100+100)/2 =100
c) Q3= 3* (n+1)/4 th observation= 38.25 th observation
38th observation= 134
39th observation= 135
38+ 0.25 * (39-38)= 134+ 0.25*( 135-134) =134.25
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