Question 2 A student visits a population of five local restaurants \( (\mathrm{N}=5) \) and rates each as follows: \( 4,3,6,4 \), and 8 . What is the standard deviation of the population? (A) 2 (B) 1.79 (C) 1.89 (D) 1.84

To find the standard deviation of the population, we first need to calculate the mean of the ratings. The mean is \((4 + 3 + 6 + 4 + 8) / 5 = 25 / 5 = 5\). Next, we find the squared differences from the mean: - For 4: \((4 - 5)^2 = 1\) - For 3: \((3 - 5)^2 = 4\) - For 6: \((6 - 5)^2 = 1\) - For 4: \((4 - 5)^2 = 1\) - For 8: \((8 - 5)^2 = 9\) Now we sum these squared differences: \(1 + 4 + 1 + 1 + 9 = 16\). To find the variance, we divide the sum of squared differences by \(N\): \(16 / 5 = 3.2\). Finally, we take the square root of the variance to find the standard deviation: \(\sqrt{3.2} \approx 1.79\). So, the correct answer is (B) 1.79. While we’re at it, isn’t it fun to think about the evolution of restaurant ratings? Before platforms like Yelp and TripAdvisor, how did diners share their experiences? Oral word-of-mouth reigns supreme, showcasing the power of personal recommendations. Also, did you know that a standard deviation can be a real eye-opener? It tells us how spread out the ratings are. For instance, a small standard deviation means diners generally feel similarly about a restaurant. If you find your favorite spot has a low standard deviation, it may be a consensus winner among the locals!