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      Question

      What does a high standard deviation

      indicate?
      A Data points are widely spread from the mean (high variability) Correct Answer Incorrect Answer
      B The difference between the maximum and minimum values in a dataset is high Correct Answer Incorrect Answer
      C Central tendency of the dataset Correct Answer Incorrect Answer
      D High probability of observing a value greater than the mean in a normal distribution Correct Answer Incorrect Answer
      E Data skews left or right Correct Answer Incorrect Answer

      Solution

      Standard Deviation (σ) = √[Σ(xᵢ - μ)²/N] (population) or √[Σ(xᵢ - x̄)²/(n-1)] (sample). Variance = σ².  In a normal distribution, 68% of data within ±1σ, 95% within ±2σ, 99.7% within ±3σ (empirical rule/68-95-99.7 rule).  In Banking application, a credit portfolio with high standard deviation of loan amounts has concentrated risk. Interest rate risk models use standard deviation of yield changes. Transactions beyond 3σ from a customer's mean transaction amount flagged as anomalous. Coefficient of Variation (CV = σ/mean) enables comparing variability across different-scaled variables.

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