The class sizes of the introductory psychology courses at a college are shown below 121,134,106,93,149,130,119,128 the college a
dds a new honors introductory psychology course with 45 student. What effect does the new class size have on the center and spread of the class sizes of the introductory psychology courses at the college?
The college adds a new Honors Introductory Psychology course with 45 students. What effect does the new class size have on the center and spread of the class sizes of the Introductory Psychology courses at the college?
Center : Mean Before the introduction of the new course, center = average(121,134,106,93,149,130,119,128) = 122.5 After the introduction of the new course, center = average(121,134,106,93,149,130,119,128,45) = 113.9 The center has moved to the left (if plotted in a graph) because of the low intake for the new course. Spread before introduction of the new course : Arrange the numbers in ascending order: (93, 106,119, 121), (128, 130,134, 149) Q1=median(93,106,119,121) = 112.5 Q3=median(128,130,134,149) = 132 Spread = Interquartile range = Q3-Q1 = 19.5 After addition of the new course,
(45,93, 106,119,) 121, (128, 130,134, 149) Q1=median(45,93,106,119)=99.5 Q3=median (128, 130,134, 149)= 132 Spread = Interquartile range = 132-99.5 =32.5 We see that the spread has increased after the addition of the new course.
We can use the central angle theorem for this. It says that an angle inscribed in a circle (on the circumference) measured half of the arc it intercepts (by 2 points on the circumference of the circle).
<em>that would mean that Angle KAW is </em><em>half </em><em>of measure of Arc KW.</em> Thus we can write:
m∠A = 0.5 (arc KE + arc EW)
x+45 =0.5 (x+20+3x)
x+45 = 0.5(4x+20)
x+45 = 2x + 10
45 - 10 = 2x - x
Thus, x = 35
<em>Since Arc KW = Arc KE + Arc EW and x = 35, we can say:</em>
