The frequency table shows the reaction time, t seconds, for a chemical to change the colour of the litmus paper in 100 laboratory sessions. Calculate an estimate for the

1. Find the class midpoints and calculate the estimated mean.

Midpoints: $0.5,\ 1.5,\ 2.5,\ 3.5,\ 4.5$

$\text{Estimated mean}=\frac{0.5(8)+1.5(28)+2.5(44)+3.5(18)+4.5(2)}{100}$

$=\frac{4+42+110+63+9}{100}$

$=\frac{228}{100}=2.28$

1. Use class midpoints and the estimated mean to calculate the standard deviation.

Class midpoints: $0.5,\ 1.5,\ 2.5,\ 3.5,\ 4.5$

Using $\bar{x}=2.37$ and $\sum f=100$,

$\sigma=\sqrt{\frac{\sum f(x-\bar{x})^2}{\sum f}}$

$=\sqrt{\frac{8(0.5-2.37)^2+28(1.5-2.37)^2+44(2.5-2.37)^2+18(3.5-2.37)^2+2(4.5-2.37)^2}{100}}$

$=0.923\ldots$