2009-I-10

$\begin{array}{cl}
= & \dfrac{25 + 27}{2} \\
= & 26 \text{ words per minute}
\end{array}$

The range

$\begin{array}{cl}
= & 39 – 12 \\
= & 27 \text{ words per minute}
\end{array}$

The lower quartile

$\begin{array}{cl}
= & \dfrac{21 + 21}{2} \\
= & 21 \text{ words per minute}
\end{array}$

The upper quartile

$\begin{array}{cl}
= & \dfrac{35+35}{2} \\
= & 35 \text{ words per minute}
\end{array}$

The inter-quartile range

$\begin{array}{cl}
= & 35 – 21 \\
= & 14 \text{ words per minute}
\end{array}$

1. The range of the typing speed after training

   $\begin{array}{cl}
   = & 52 – 27 \\
   = & 25 \text{ words per minute}
   \end{array}$

   Since the range of the typing speed after training is smaller than that before training, then the distribution of the typing speed after training is not more dispersed than that before the training.

2. Note that the slowest typing speed after training is $27\text{ words per minute}$, which is faster than the median of the typing speed before training. Therefore, not less than half of the students show improvement. Yes, I agree.