7 The histogram shows the age distribution of people living in Inner London in 2001.\\
\includegraphics[max width=\textwidth, alt={}, center]{aabf9d8b-5f91-4a3b-bcf8-e46cb45127c4-4_805_1372_392_401}

Data sourced from he 2001 Census, \href{http://www.statistics.gov.uk}{www.statistics.gov.uk}
\begin{enumerate}[label=(\roman*)]
\item State the type of skewness shown by the distribution.
\item Use the histogram to estimate the number of people aged under 25.
\item The table below shows the cumulative frequency distribution.

\begin{center}
\begin{tabular}{ | l | c | c | c | c | c | c | }
\hline
Age & 20 & 30 & 40 & 50 & 65 & 100 \\
\hline
Cumulative frequency (thousands) & 660 & 1240 & 1810 & $a$ & 2490 & 2770 \\
\hline
\end{tabular}
\end{center}

(A) Use the histogram to find the value of $a$.\\
(B) Use the table to calculate an estimate of the median age of these people.

The ages of people living in Outer London in 2001 are summarised below.

\begin{center}
\begin{tabular}{ | l | c | c | c | c | c | c | }
\hline
Age ( $x$ years) & $0 \leqslant x < 20$ & $20 \leqslant x < 30$ & $30 \leqslant x < 40$ & $40 \leqslant x < 50$ & $50 \leqslant x < 65$ & $65 \leqslant x < 100$ \\
\hline
Frequency (thousands) & 1120 & 650 & 770 & 590 & 680 & 610 \\
\hline
\end{tabular}
\end{center}
\item Illustrate these data by means of a histogram.
\item Make two brief comments on the differences between the age distributions of the populations of Inner London and Outer London.
\item The data given in the table for Outer London are used to calculate the following estimates.

Mean 38.5, median 35.7, midrange 50, standard deviation 23.7, interquartile range 34.4.\\
The final group in the table assumes that the maximum age of any resident is 100 years. These estimates are to be recalculated, based on a maximum age of 105, rather than 100. For each of the five estimates, state whether it would increase, decrease or be unchanged.\\[0pt]
[4]
\end{enumerate}

\hfill \mbox{\textit{OCR MEI S1  Q7 [20]}}