Doubtify – JEE Ki Taiyaari, Simple Bhasha Mein

  ❓ Question FOR: The mean and standard deviation of 100 observations are 40 and 5.1 , respectively. By mistake, one observation is taken as 50 instead of 40 . If the correct mean and correct standard deviation are μ \mu μ and σ \sigma σ , respectively, then the value of 10 ( μ + σ ) 10(\mu + \sigma) is equal to ? 🖼️ Question Image ✍️ Short Solution This is a standard JEE correction-type statistics question . The idea is simple: 👉 Use the given (wrong) mean and SD to compute the wrong total and wrong sum of squares . 👉 Correct the single wrong observation. 👉 Recalculate the correct mean and correct standard deviation . 🔹 Step 1 — Find the wrong total (Σx) Given: Number of observations, n = 100 n = 100 Wrong mean = 40 = 40 So, Σ x wrong = 100 × 40 = 4000 \Sigma x_{\text{wrong}} = 100 \times 40 = 4000 One value was taken as 50 instead of 40 . Correct total: Σ x correct = 4000 − 50 + 40 = 3990 \Sigma x_{\text{correct}} = 4000 - 50 + 40 = 3990 ...