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Find the correct Statement :Statement-1 ...

Find the correct Statement :Statement-1 : The S.D. of 5 scores 1 2 3 4 5 is `sqrt2`.
Statement-2 : S.D. =`sqrt"variance"`

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To solve the problem, we need to evaluate the two statements regarding the standard deviation (S.D.) of the given scores and the relationship between standard deviation and variance. ### Step-by-step Solution: **Step 1: Understand the Statements** - **Statement 1**: The standard deviation of the scores 1, 2, 3, 4, 5 is `sqrt(2)`. - **Statement 2**: Standard deviation (S.D.) = `sqrt(variance)`. **Step 2: Verify Statement 2** - The second statement is a fundamental property of statistics. The standard deviation is indeed defined as the square root of the variance. Therefore, Statement 2 is **correct**. **Step 3: Calculate the Mean of the Scores** - The scores are 1, 2, 3, 4, and 5. - Mean (μ) = (1 + 2 + 3 + 4 + 5) / 5 - Mean (μ) = 15 / 5 = 3. **Step 4: Calculate the Deviations from the Mean** - Now, we calculate the deviations of each score from the mean: - For 1: 1 - 3 = -2 - For 2: 2 - 3 = -1 - For 3: 3 - 3 = 0 - For 4: 4 - 3 = 1 - For 5: 5 - 3 = 2 **Step 5: Square the Deviations** - Now, we square each of these deviations: - (-2)² = 4 - (-1)² = 1 - (0)² = 0 - (1)² = 1 - (2)² = 4 **Step 6: Calculate the Sum of Squared Deviations** - Sum of squared deviations = 4 + 1 + 0 + 1 + 4 = 10. **Step 7: Calculate the Variance** - Variance (σ²) = (Sum of squared deviations) / (Number of observations) - Variance (σ²) = 10 / 5 = 2. **Step 8: Calculate the Standard Deviation** - Standard Deviation (σ) = `sqrt(variance)` = `sqrt(2)`. **Step 9: Verify Statement 1** - Statement 1 claims that the standard deviation is `sqrt(2)`, which we have calculated to be true. ### Conclusion: Both statements are correct: - **Statement 1**: Correct (S.D. = `sqrt(2)`) - **Statement 2**: Correct (S.D. = `sqrt(variance)`)
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