Basel is a keen learner of languages. He finds a website on which a large number of language tutors offer their services. Basel records the cost, in dollars, of a one hour lesson from a random sample of tutors. He puts the data into a computer program which gives the following summary statistics.

Cost per 1 hour lesson
Min.    :10.0
1st Qu. :16.0
Median  :17.2
Mean    :19.8
3rd Qu. :21.0
Max.    :40.0

\begin{enumerate}[label=(\alph*)]
\item Showing all calculations, comment on any outliers for the cost of a one hour lesson with a language tutor. [4]

\item Describe the skewness of the data and explain what it means in this context. [2]
\end{enumerate}

Dafydd is also a keen learner of languages. He takes his own random sample of the cost, in dollars, for a one hour lesson. He produces the following box plot.

\includegraphics{figure_6}

\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item 
\begin{enumerate}[label=(\roman*)]
\item What will happen to the mean if the outlier is removed?
\item What will happen to the median if the outlier is removed? [2]
\end{enumerate}

\item Compare and contrast the distributions of the cost of one hour language lessons for Dafydd's sample and Basel's sample. [2]
\end{enumerate}

\hfill \mbox{\textit{WJEC Unit 2 2018 Q06 [10]}}