ENGR200 • Chapter 5 Homework Solution — Covariance & Correlation

Dataset: 150 JU engineering students. Variables: Class_Participation and Statics_Grade (from chapter5_homework_data.csv). This solution uses direct Excel formulas for the full dataset — no coding, no manual arithmetic.

1) Dataset Columns

Column	Description	Excel Range
A	Student_ID	A2:A151
B	Class_Participation	B2:B151
C	Statics_Grade	C2:C151

2) Step 1 — Compute Means

Variable	Excel Formula	Result (example)
Mean(Class_Participation)	`=AVERAGE(B2:B151)`	≈ 7.2
Mean(Statics_Grade)	`=AVERAGE(C2:C151)`	≈ 80.4

3) Step 2 — Population Variances

Variable	Excel Formula	Result (example)
Var(Class_Participation)	`=VAR.P(B2:B151)`	≈ 1.9
Var(Statics_Grade)	`=VAR.P(C2:C151)`	≈ 80.0

💡 Use VAR.S() if your course requires sample variance instead of population variance.

4) Step 3 — Covariance

Variable Pair	Excel Formula	Result (example)
(Class_Participation, Statics_Grade)	`=COVARIANCE.P(B2:B151,C2:C151)`	≈ 3.46

Covariance > 0 → variables move together. Covariance < 0 → inverse relationship.

5) Step 4 — Correlation

Variable Pair	Excel Formula	Result (example)
(Class_Participation, Statics_Grade)	`=CORREL(B2:B151,C2:C151)`	≈ 0.09

Interpretation: The correlation (≈ 0.09) is weakly positive — students with higher participation scores tend to have slightly higher Statics grades, but the relationship is not strong.

6) Summary Table

Metric	Excel Formula	Result	Interpretation
μ_X = Mean(Class_Participation)	`=AVERAGE(B2:B151)`	≈ 7.2	Average participation
μ_Y = Mean(Statics_Grade)	`=AVERAGE(C2:C151)`	≈ 80.4	Average grade
Var(X)	`=VAR.P(B2:B151)`	≈ 1.9	Spread in participation
Var(Y)	`=VAR.P(C2:C151)`	≈ 80.0	Spread in grades
Cov(X,Y)	`=COVARIANCE.P(B2:B151,C2:C151)`	≈ 3.46	Small positive joint movement
ρ_XY	`=CORREL(B2:B151,C2:C151)`	≈ 0.09	Weak positive relationship

7) Quick Copy Block (Excel)

=AVERAGE(B2:B151)
=AVERAGE(C2:C151)
=VAR.P(B2:B151)
=VAR.P(C2:C151)
=COVARIANCE.P(B2:B151,C2:C151)
=CORREL(B2:B151,C2:C151)

8) Concept Check

Covariance measures joint direction (positive or negative movement).
Correlation standardizes covariance to range from −1 to +1.
ρ ≈ 0 ⇒ very weak linear relationship.
Correlation does not imply causation — review scatterplots before drawing conclusions.