Project 1 • Page 300 Exercise
Comparative Dispersion in Mathematics
Assessing score variation and academic stability across Optional and Compulsory Mathematics cohorts using standard deviation and C.V.
👥 Sample: N = 61 Students📈 Metric: Coefficient of Variation (C.V.)
Step 1
Optional Math Grouped Frequency Data
| Marks (x) | f | Mid (m) | d=(m-35)/10 | fd | fd² |
|---|
| 0-10 | 0 | 5 | -3 | 0 | 0 |
| 10-20 | 6 | 15 | -2 | -12 | 24 |
| 20-30 | 5 | 25 | -1 | -5 | 5 |
| 30-40 | 18 | 35 | 0 | 0 | 0 |
| 40-50 | 13 | 45 | 1 | 13 | 13 |
| 50-60 | 6 | 55 | 2 | 12 | 24 |
| 60-70 | 7 | 65 | 3 | 21 | 63 |
| 70-80 | 6 | 75 | 4 | 24 | 96 |
Sum of Deviations
Σfd = 53
Sum of Squared Deviations
Σfd² = 225
Step 2
Mathematical Results for Optional Math
Calculated Mean
43.69
Σfm / N = 2665 / 61
Standard Deviation
17.14
σ = √(225/61 - (53/61)²) × 10
Coefficient of Variation
39.24%
(σ / x̄) × 100%
Synthesis
Comparative Decision Framework
Consistency Criterion: Lower C.V. denotes uniform marks.
Variability Indicator: Higher C.V. reflects wide spread.
Curricular Benchmark: Compare 39.24% with compulsory data.
Core Insight
Optional Mathematics exhibits moderate variability. Students display diverse mastery across basic and advanced subject modules.