Calculate the mean deviation from the mean of the distribution below

To calculate the mean deviation from the mean, we'll use the formula provided: MD = f|x - x| f. First, we need to find the class mark (x) for each class, then calculate the mean (x), and finally apply the mean deviation formula. Assumption: For the class "10-10", we will take the class mark (x) as 10. For the other classes, the class mark is the midpoint of the interval. Here's a table with the necessary calculations: | Class | Freq (f) | Class Mark (x) | fx | |x - x| | f|x - x| | | :------ | :------- | :------------- | :----- | :-------------- | :--------------- | | 10-10 | 12 | 10 | 120 | 19.32 | 231.84 | | 10-20 | 25 | 15 | 375 | 14.32 | 358.00 | | 20-30 | 32 | 25 | 800 | 4.32 | 138.24 | | 30-40 | 25 | 35 | 875 | 5.68 | 142.00 | | 40-50 | 21 | 45 | 945 | 15.68 | 329.28 | | 50-60 | 10 | 55 | 550 | 25.68 | 256.80 | | Total | f = 125 | | fx = 3665 | | f|x - x| = 1456.16 | Step 1: Calculate the total frequency ( f) and the sum of fx ( fx). f = 12 + 25 + 32 + 25 + 21 + 10 = 125 fx = (12 × 10) + (25 × 15) + (32 × 25) + (25 × 35) + (21 × 45) + (10 × 55) fx = 120 + 375 + 800 + 875 + 945 + 550 = 3665 Step 2: Calculate the mean (x). x = ( fx)/( f) = (3665)/(125) = 29.32 Step 3: Calculate the absolute deviation |x - x| for each class mark. For x=10: |10 - 29.32| = 19.32 For x=15: |15 - 29.32| = 14.32 For x=25: |25 - 29.32| = 4.32 For x=35: |35 - 29.32| = 5.68 For x=45: |45 - 29.32| = 15.68 For x=55: |55 - 29.32| = 25.68 Step 4: Calculate f|x - x| for each class and sum them ( f|x - x|). f|x - x| = (12 × 19.32) + (25 × 14.32) + (32 × 4.32) + (25 × 5.68) + (21 × 15.68) + (10 × 25.68) f|x - x| = 231.84 + 358.00 + 138.24 + 142.00 + 329.28 + 256.80 = 1456.16 Step 5: Calculate the Mean Deviation (MD). MD = f|x - x| f = (1456.16)/(125) = 11.64928 Rounding to two decimal places: MD ≈ 11.65 The mean deviation from the mean is 11.65. Send me the next one 📸