Question

Consider the relationship between students’ score on a first course exam and their score on the final exam.

First-test score               Final-exam score

153                              145

144                              140

162                              145

149                              170

127                              145

118                              175

158                              170

153                              160

Using (1) your calculator, a pencil and graph paper and then (2) Excel:

1. Plot the data with the first-test score on the x axis and the final-exam score on the y axis.
2. Find the arithmetic mean, the mean absolute deviation and the standard deviation for both variables. Find the correlation between the two variables
3. Write a brief explanation of what you have found and how the statistics you calculated support your explanation.

please answer each of them clearly

Answer 1

a)

b)

	first-test	final-exam	abs dev. First -test	abs dev final-exam
	153	145	7.5	11.25
	144	140	1.5	16.25
	162	145	16.5	11.25
	149	170	3.5	13.75
	127	145	18.5	11.25
	118	175	27.5	18.75
	158	170	12.5	13.75
	153	160	7.5	3.75
mean	145.5	156.25	11.875	12.5
standard deviation	15.3715879	14.0788595
	r	-0.20133329

Formulas

	first-test	final-exam	abs dev. First -test	abs dev final-exam
	153	145	=ABS(B2-145.5)	=ABS(C2-156.25)
	144	140	=ABS(B3-145.5)	=ABS(C3-156.25)
	162	145	=ABS(B4-145.5)	=ABS(C4-156.25)
	149	170	=ABS(B5-145.5)	=ABS(C5-156.25)
	127	145	=ABS(B6-145.5)	=ABS(C6-156.25)
	118	175	=ABS(B7-145.5)	=ABS(C7-156.25)
	158	170	=ABS(B8-145.5)	=ABS(C8-156.25)
	153	160	=ABS(B9-145.5)	=ABS(C9-156.25)
mean	=AVERAGE(B2:B9)	=AVERAGE(C2:C9)	=AVERAGE(D2:D9)	=AVERAGE(E2:E9)
standard deviation	=STDEV(B2:B9)	=STDEV(C2:C9)
	r	=CORREL(B2:B9,C2:C9)

for first -test

mean = 145.5

MAD = 11.875

sd = 15.37159

for final exam

mean =156.25

MAD= 12.5

sd = 14.0789

r = -0.2013

c)

since r < 0

there is negative correlation, value of r is less than 0.3, hence it is weak correlation