Question

1. Consider the following sample of five LSAT scores:

155

155

150

180

175

     Compute the 40^th percentile score.

     (a) 155 (b) 160 (c) 160.5 (d) 167.5 (e) none of these responses

2. Consider the below data on years of education and earnings.

Years of Education	13	17	12	21	22
Earnings (in 1000’s)	$25	$55	$20	$80	$100

     Compute the correlation coefficient between years of education and earnings.

     (a) .793 (b) -.922 (c) 3.96 (d) .922 (e) .990

Answer 1

Solution :

1)

From given data :

150 , 155 , 155 , 175 , 180

40th percentile = 155

2)

X	Y	XY	X^2	Y^2
13	25	325	169	625
17	55	935	289	3025
12	20	240	144	400
21	80	1680	441	6400
22	100	2200	484	10000

n	5
sum(XY)	5380.00
sum(X)	85.00
sum(Y)	280.00
sum(X^2)	1527.00
sum(Y^2)	20450.00
Numerator	3100.00
Denominator	3127.06
r	0.990
r square	0.9828
Xbar(mean)	17.0000
Ybar(mean)	56.0000
SD(X)	4.0497
SD(Y)	30.8869
b	7.5610
a	-72.5366

r = 0.990

Option E)