1. **State the problem:** Find the mean $\bar{x}$ and standard deviation $s$ from the grouped frequency table with given class intervals and frequencies. \n\n2. **Calculate midpoints for each class interval:** The midpoint $x_i$ is $$x_i = \frac{\text{Lower Limit} + \text{Upper Limit}}{2}.$$ \nClass midpoints: \n- $(8+11)/2 = 9.5$ \n- $(12+15)/2 = 13.5$ \n- $(16+19)/2 = 17.5$ \n- $(20+23)/2 = 21.5$ \n- $(24+27)/2 = 25.5$ \n- $(28+31)/2 = 29.5$ \n- $(32+35)/2 = 33.5$ \n\n3. **Calculate $f x_i$ and $f x_i^2$ for each class:** multiply frequencies by midpoints and squared midpoints. \n- For $x_i^2$, square each midpoint. \nCalculate: \n$f x_i$: $f_i \times x_i$ \n$f x_i^2$: $f_i \times x_i^2$ \n\n| $x_i$ | $f_i$ | $f_i x_i$ | $x_i^2$ | $f_i x_i^2$ |\n|-------|-------|---------|---------|-------------|\n| 9.5 | 11 | 104.5 | 90.25 | 992.75 |\n| 13.5 | 7 | 94.5 | 182.25 | 1275.75 |\n| 17.5 | 11 | 192.5 | 306.25 | 3368.75 |\n| 21.5 | 24 | 516 | 462.25 | 11094 |\n| 25.5 | 14 | 357 | 650.25 | 9103.5 |\n| 29.5 | 11 | 324.5 | 870.25 | 9572.75 |\n| 33.5 | 12 | 402 | 1122.25 | 13467 |\n\n4. **Calculate totals:** \n- Total frequency $N=11+7+11+24+14+11+12=90$ \n- Total $\sum f x_i = 104.5+94.5+192.5+516+357+324.5+402=1991$ \n- Total $\sum f x_i^2 = 992.75+1275.75+3368.75+11094+9103.5+9572.75+13467=48875.25$ \n\n5. **Calculate the mean $\bar{x}$:** $$\bar{x} = \frac{\sum{f x_i}}{N} = \frac{1991}{90} \approx 22.12.$$ \n\n6. **Calculate variance $s^2$: $$s^2 = \frac{\sum f x_i^2}{N} - \bar{x}^2 = \frac{48875.25}{90} - (22.12)^2.$$ \nCalculate components: $$\frac{48875.25}{90} \approx 542.00,$$ $$22.12^2 = 489.29.$$ \nSo, $$s^2 = 542.00 - 489.29 = 52.71.$$ \n\n7. **Calculate standard deviation $s$: $$s = \sqrt{52.71} \approx 7.26.$$ \n\n**Final answers:** \n\n$$\bar{x} \approx 22.12,$$ \n$$s \approx 7.26.$$