To calculate the mean and standard deviation from the given frequency distribution, we will use the following formulas: Mean ($\bar{x}$) $$ \bar{x} = \frac{\sum fx}{\sum f} $$ Standard Deviation ($\sigma$) $$ \sigma = \sqrt{\frac{\sum fx^2}{\sum f} - \left(\frac{\sum fx}{\sum f}\right)^2} $$ First, let's create a table to organize the calculations for $fx$ and $fx^2$. The total number of students is $\sum f = 50$. | Hours per day ($x$) | Number of students ($f$) | $fx$ | $x^2$ | $fx^2$ | |---------------------|--------------------------|------|-------|--------| | 4 | 5 | 20 | 16 | 80 | | 5 | 7 | 35 | 25 | 175 | | 6 | 5 | 30 | 36 | 180 | | 7 | 9 | 63 | 49 | 441 | | 8 | 12 | 96 | 64 | 768 | | 9 | 4 | 36 | 81 | 324 | | 10 | 3 | 30 | 100 | 300 | | 11 | 5 | 55 | 121 | 605 | | Total | 50 | 365 | | 2873 | From the table, we have: $\sum f = 50$ $\sum fx = 365$ $\sum fx^2 = 2873$ a) Mean Step 1: Use the formula for the mean. $$ \bar{x} = \frac{\sum fx}{\sum f} $$ Step 2: Substitute the calculated values into the formula. $$ \bar{x} = \frac{365}{50} $$ Step 3: Calculate the mean. $$ \bar{x} = 7.3 $$ The mean is 7.30 hours (correct to two decimal places). $$\boxed{\text{Mean} = 7.30}$$ b) Standard Deviation Step 1: Use the formula for the standard deviation. $$ \sigma = \sqrt{\frac{\sum fx^2}{\sum f} - \left(\frac{\sum fx}{\sum f}\right)^2} $$ Step 2: Substitute the calculated values into the formula. $$ \sigma = \sqrt{\frac{2873}{50} - \left(\frac{365}{50}\right)^2} $$ Step 3: Perform the division and squaring. $$ \sigma = \sqrt{57.46 - (7.3)^2} $$ $$ \sigma = \sqrt{57.46 - 53.29} $$ Step 4: Subtract the values. $$ \sigma = \sqrt{4.17} $$ Step 5: Calculate the square root and round to two decimal places. $$ \sigma \approx 2.04205778 $$ $$ \sigma \approx 2.04 $$ The standard deviation is 2.04 hours (correct to two decimal places). $$\boxed{\text{Standard Deviation} = 2.04}$$ That's 2 down. 3 left today — send the next one.