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ScanSolve AI Answer
Here's an explanation of the columns in your frequency table: x_i (Variable Value): These are the distinct data points or categories. f_i (Frequency): This shows how many times each x_i value appears. CF (Cumulative Frequency): This is the running total of frequencies, indicating the count of observations less than or equal to the current x_i. x_i f_i (Product): This is the product of each x_i and its f_i, used for calculating the mean. Let's solve for the mode, mean, and median using the provided table. The data from the table is: | x_i | f_i | CF | x_i f_i | | :---: | :---: | :---: | :---: | | 2 | 2 | 2 | 4 | | 4 | 1 | 3 | 4 | | 6 | 5 | 8 | 30 | | 7 | 7 | 15 | 49 | | 9 | 3 | 18 | 27 | | 12 | 2 | 20 | 24 | | Total | 20 | | 138 | a) What is the mode? Step 1: Identify the highest frequency The highest value in the f_i column is 7. Step 2: Find the corresponding x_i value The x_i value corresponding to the frequency of 7 is 7. The mode is 7. b) Mean Step 1: Use the formula for the mean The mean (x) is given by the sum of x_i f_i divided by the sum of f_i. x = ( x_i f_i)/( f_i) Step 2: Substitute the sums from the table From the table, x_i f_i = 138 and f_i = 20. x = (138)/(20) Step 3: Calculate the mean x = 6.9 The mean is 6.9. c) Median Step 1: Determine the position of the median The total number of observations is N = f_i = 20. Since N is even, the median is the average of the (N)/(2)-th and ((N)/(2)+1)-th values. (N)/(2) = (20)/(2) = 10 We need the 10th and 11th values. Step 2: Find the values using cumulative frequency (CF) Looking at the CF column: The 10th value falls within the range where CF is 15, which corresponds to x_i = 7. The 11th value also falls within this range, corresponding to x_i = 7. The 10th value is 7. The 11th value is 7. Step 3: Calculate the median Median = (7+7)/(2) = 7 The median is 7. d) Draw a frequency table to show the distribution Here is the frequency table: | x_i | f_i | CF | x_i f_i | | :---: | :---: | :---: | :---: | | 2 | 2 | 2 | 4 | | 4 | 1 | 3 | 4 | | 6 | 5 | 8 | 30 | | 7 | 7 | 15 | 49 | | 9 | 3 | 18 | 27 | | 12 | 2 | 20 | 24 | | Total | 20 | | 138 | Send me the next one 📸