Class 10 Mathematics Chapter 11 Information Handling Unit Wise Class Test 2 – Exercise 11.2 & Review Exercise

Step 1: μ = (1 + 2 + 3)/3 = 2.

Step 2: Σ(x − μ)² = (−1)² + 0² + 1² = 2.

Step 3: σ² = 2/3.

Answer: (b) 2/3

Step 1: First 20 primes: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71.

Step 2: Range = 71 − 2 = 69

Largest = 30, smallest = 15.

Range = 30 − 15 = 15

Step 1 – Mean: Σx = 250, n = 5, x̄ = 50.0

Step 2 – Deviations:

Step 3 – Variance: σ² = 0.10/5 = 0.02

Step 4 – SD: σ = √0.02 ≈ 0.141 cm

Step 5 – CV: (0.141/50) × 100 ≈ 0.28%

Conclusion: The SD is tiny compared with the mean, so the rods are very consistent.

Step 1 – Mean: Σx = 63, n = 7, x̄ = 9

Step 2 – Deviations:

Step 3 – Variance: σ² = 56/7 = 8

(Sample: 56/6 ≈ 9.33)

Step 1: Σx = 372, n = 7; Σx² = 2704 + 3025 + 2500 + 2809 + 2916 + 3136 + 2704 = 19794.

Step 2 – Mean: x̄ = 372/7 ≈ 53.14

Step 3 – Variance: σ² = 19794/7 − (372/7)² = 2827.714 − 2824.163 = 174/49 ≈ 3.55

Step 4 – SD: σ = √3.551 ≈ 1.88

(Sample: s² ≈ 4.14, s ≈ 2.04)

Step 1: x̄ = 210/6 = 35

Step 2: σ² = 7560/6 − 35² = 1260 − 1225 = 35

Step 3: σ = √35 ≈ 5.92

Step 1 – Mean: Σx = 80, n = 5, x̄ = 16

Step 2 – Deviations:

Step 3 – Variance: σ² = 34/5 = 6.8

Step 4 – SD: σ = √6.8 ≈ 2.61 million

Step 5: Range = 20 − 13 = 7 million; CV = (2.61/16) × 100 ≈ 16.3%

Conclusion: Sales predictions typically vary by about Rs 2.61 million (≈16%) around the mean of Rs 16 million.

(Sample: s² = 8.5, s ≈ 2.92)

Step 1 – Mean: Σx = 27.7, n = 5, x̄ = 5.54

Step 2 – Deviations:

Step 3 – Variance: σ² = 1.312/5 = 0.2624

Step 4 – SD: σ = √0.2624 ≈ 0.51%

Step 5: CV = (0.51/5.54) × 100 ≈ 9.2%; range = 6.2 − 4.8 = 1.4%.

Conclusion: The spread is small relative to the mean, so unemployment is fairly balanced across the provinces.

(Sample: s ≈ 0.57%)