Statistics and Probability — Flashcards
Tamil Nadu Board · Class 10 · Mathematics
24 flashcards for Statistics and Probability (Tamil Nadu Board Class 10 Mathematics) to test yourself on key terms and facts.
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Calculate the mean of the following data: 25, 30, 35, 40, 45
Answer
Step 1: Add all observations = 25 + 30 + 35 + 40 + 45 = 175 Step 2: Count the number of observations = 5 Step 3: Apply formula: Mean = Sum/n = 175/5 = 35 Answer: The mean is 35…
Find the range and coefficient of range from the data: 12, 45, 23, 67, 18, 39
Answer
Step 1: Identify largest value (L) = 67 and smallest value (S) = 12 Step 2: Calculate Range = L - S = 67 - 12 = 55 Step 3: Calculate Coefficient of Range = (L - S)/(L + S) = 55/(67 + 12) = 55/79 ≈ 0.6…
When do you use the standard deviation formula: σ = √[Σx²/n - (Σx/n)²]?
Answer
Use this 'direct method' formula when: 1. You have ungrouped data given directly as individual values 2. You need to find how spread out the values are from the mean 3. Calculating squared deviations …
The standard deviation of TV watching hours is: 6, 7, 8, 9, 10, 11, 12 with frequencies 3, 6, 9, 13, 8, 5, 4. Calculate the mean.
Answer
Step 1: Create table with xᵢ and fᵢ values Step 2: Calculate xᵢfᵢ for each: 18, 42, 72, 117, 80, 55, 48 Step 3: Sum xᵢfᵢ = 432 and sum fᵢ = 48 Step 4: Apply Mean formula = Σxᵢfᵢ/N = 432/48 = 9 Answer:…
Find the standard deviation of grouped data: Classes 0-10, 10-20, 20-30, 30-40 with frequencies 8, 12, 17, 14 (Assume mean = 20.5)
Answer
Step 1: Find class midpoints: 5, 15, 25, 35 Step 2: Calculate deviations from mean: dᵢ = xᵢ - 20.5 = -15.5, -5.5, 4.5, 14.5 Step 3: Calculate fᵢdᵢ²: 8(240.25) = 1922, 12(30.25) = 363, 17(20.25) = 344.
When the original data is 2, 3, 5, 7, 8 with σ = 2.28, what happens to standard deviation when you multiply each value by 4?
Answer
When you multiply all data values by a constant k, the standard deviation also gets multiplied by k. Original data: 2, 3, 5, 7, 8, σ₁ = 2.28 New data: 8, 12, 20, 28, 32 (multiplied by 4) New σ₂ = 4 ×…
Calculate the variance of the first 5 natural numbers: 1, 2, 3, 4, 5
Answer
Step 1: Calculate mean = (1+2+3+4+5)/5 = 15/5 = 3 Step 2: Find deviations from mean and square them: (1-3)² = 4, (2-3)² = 1, (3-3)² = 0, (4-3)² = 1, (5-3)² = 4 Step 3: Sum of squared deviations = 4 + …
Mean = 25.6, Coefficient of Variation = 18.75%. Find the standard deviation.
Answer
Use the coefficient of variation formula: C.V. = (σ/mean) × 100% Step 1: Substitute known values 18.75 = (σ/25.6) × 100 Step 2: Rearrange to find σ σ = (18.75 × 25.6)/100 σ = 480/100 σ = 4.8 Answer…
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