Question

delve into the world of film criticism by analyzing the meta_score. these statistical measures offer a deeper understanding of how variable to calculate the range, variance, and standard deviation. click the icon to view the subset of the imdb dataset. 1. what is the range? what does that tell us? the range is 38, indicating the span between the highest and lowest ratings. (round to one decimal place as needed.) 2. what is the standard deviation? the standard deviation is (round to three decimal places as needed.) 3. describe the spread and what that tells us about how films are appraised by critics. the standard deviation signifies that the average distance of individual ratings from the mean rating is (round to three decimal places as needed.)

Explanation:

Step1: Recall formula for standard - deviation

For a sample of data \(x_1,x_2,\cdots,x_n\), the mean \(\bar{x}=\frac{1}{n}\sum_{i = 1}^{n}x_i\), and the sample standard - deviation \(s=\sqrt{\frac{\sum_{i = 1}^{n}(x_i-\bar{x})^2}{n - 1}}\). First, we need to find the mean of the data set.

Step2: Calculate the mean

Let the data set be \(x_1,x_2,\cdots,x_n\). Assume \(n\) is the number of data points. Add up all the data points and divide by \(n\).

Step3: Calculate the squared - differences

For each data point \(x_i\), calculate \((x_i-\bar{x})^2\). Then sum up all these squared - differences \(\sum_{i = 1}^{n}(x_i-\bar{x})^2\).

Step4: Calculate the standard - deviation

Divide the sum of squared - differences by \(n - 1\) and then take the square root: \(s=\sqrt{\frac{\sum_{i = 1}^{n}(x_i-\bar{x})^2}{n - 1}}\). Round the result to three decimal places.

Since the data set is not provided in the text (only the problem - statement about calculating standard deviation is shown), we cannot give a numerical answer. But if we had the data set \(x_1,x_2,\cdots,x_n\):

1. First, calculate the mean \(\bar{x}=\frac{\sum_{i=1}^{n}x_i}{n}\).
2. Then, calculate \((x_i - \bar{x})^2\) for each \(i\) from \(1\) to \(n\) and sum them up: \(S=\sum_{i = 1}^{n}(x_i-\bar{x})^2\).
3. Finally, \(s=\sqrt{\frac{S}{n - 1}}\).

Answer:

Cannot be determined without the data set.