Fundamentals of Mathematical Statistics (BCA) 1st Sem Previous Year Solved Question Paper 2022

To calculate the standard deviation and coefficient of variation, you need to follow these steps:

Mean (μ) = Σ (m * f) / Σ f

Where:
m = Midpoint of the class
f = Frequency

μ = (10*4 + 12*6 + 14*10 + 16*15 + 18*9 + 20*4 + 22*2) / (4 + 6 + 10 + 15 + 9 + 4 + 2)

μ = (40 + 72 + 140 + 240 + 162 + 80 + 44) / 80

μ = 778 / 80

μ = 9.725

Variance (σ²) = Σ [(m - μ)² * f] / Σ f

σ² = [(10 - 9.725)² * 4 + (12 - 9.725)² * 6 + (14 - 9.725)² * 10 + (16 - 9.725)² * 15 + (18 - 9.725)² * 9 + (20 - 9.725)² * 4 + (22 - 9.725)² * 2] / 80

σ² ≈ (0.075625 * 4 + 0.052025 * 6 + 0.189225 * 10 + 39.015625 * 15 + 71.346225 * 9 + 108.428025 * 4 + 153.953025 * 2) / 80

σ² ≈ (0.3025 + 0.31215 + 1.89225 + 585.234375 + 642.115025 + 433.7121 + 307.90605) / 80

σ² ≈ 2973.474325 / 80

σ² ≈ 37.1684291

Standard Deviation (σ) is the square root of the variance:

σ = √(σ²)

σ ≈ √(37.1684291)

σ ≈ 6.1019 (approximately)

Step 4: Calculate the Coefficient of Variation:
Coefficient of Variation (CV) is given by (σ / μ) * 100
CV = (6.1019 / 9.725) * 100

CV ≈ 62.65% (approximately)

So, the standard deviation is approximately 6.1019, and the coefficient of variation is approximately 62.65%.