1.1. Lucy is working with some grouped, continuous data. For a set of 100 items of data, she has calculated that $\sumxf=357$ and $\sum{(x-\overset{¯}{x})}^{2}f=42$, where $f$ is the frequency for each group.

(i) Give a reason why Lucy has decided to group her data.

(ii) Briefly explain what is meant by $\sumxf$ and $\sum{(x-\overset{¯}{x})}^{2}f$.

1.2. To calculate the standard deviation, Lucy could choose to use either of the following two formulae.

standard deviation = $\sqrt{\frac{\sum{(x-\overset{¯}{x})}^{2}f}{\sumf}}or\sqrt{\frac{\sum{x}^{2}f}{\sumf}}-{\overset{¯}{x}}^{2}where\overset{¯}{x}=\frac{\sumxf}{\sumf}$

(i) Calculate the mean of Lucy's data.

(ii) Using the appropriate formula from above, calculate the standard deviation of Lucy's data.