This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
To calculate the standard deviation and variance, we first need to find the mean of the distribution. We will use a table to organize our calculations. Step 1: Create a table to calculate f, fx, and fx^2. Let x be the Age and f be the Frequency. | Age (x) | Frequency (f) | fx | x^2 | fx^2 | | :------ | :------------ | :-- | :---- | :----- | | 6 | 4 | 24 | 36 | 144 | | 7 | 6 | 42 | 49 | 294 | | 8 | 10 | 80 | 64 | 640 | | 9 | 11 | 99 | 81 | 891 | | 10 | 8 | 80 | 100 | 800 | | 11 | 1 | 11 | 121 | 121 | | Total | 40 | 336 | | 2890 | From the table: f = 40 fx = 336 fx^2 = 2890 Step 2: Calculate the mean (x). The formula for the mean of a frequency distribution is: x = ( fx)/( f) x = (336)/(40) x = 8.4 Step 3: Calculate the variance (^2). The formula for the variance of a frequency distribution is: ^2 = ( fx^2)/( f) - x^2 Substitute the values: ^2 = (2890)/(40) - (8.4)^2 ^2 = 72.25 - 70.56 ^2 = 1.69 The variance is 1.69. Step 4: Calculate the standard deviation (). The standard deviation is the square root of the variance: = sqrt(^2) = sqrt(1.69) = 1.3 The standard deviation is 1.3. That's 2 down. 3 left today — send the next one.