Compare or interpret cumulative frequency graphs

5 The numbers of births, in thousands, to mothers of different ages in England and Wales, in 1991 and 2001 are illustrated by the cumulative frequency curves. Cumulative frequency (000's) \includegraphics[max width=\textwidth, alt={}, center]{dfad6626-75ca-4dbd-9c45-42f809c163f3-3_949_1338_461_479}

1. In which of these two years were there more births? How many more births were there in this year?
2. The following quantities were estimated from the diagram.

   Year	M edian age (years)	Interquartile range (years)	Proportion of mothers giving birth aged below 25	Proportion of mothers giving birth aged 35 or above
   1991	27.5	7.3	\(33 \%\)	\(9 \%\)
   2001				\(18 \%\)

   1. Find the values missing from the table.
   2. Did the women who gave birth in 2001 tend to be younger or older or about the same age as the women who gave birth in 1991? Using the table and your values from part (a), give two reasons for your answer.

6 \includegraphics[max width=\textwidth, alt={}, center]{2fb25fc5-0445-44fa-a23e-647d14b1a376-3_803_1180_1018_413} The diagram shows the cumulative frequency graphs for the marks scored by the candidates in an examination. The 2000 candidates each took two papers; the upper curve shows the distribution of marks on paper 1 and the lower curve shows the distribution on paper 2. The maximum mark on each paper was 100.

1. Use the diagram to estimate the median mark for each of paper 1 and paper 2.
2. State with a reason which of the two papers you think was the easier one.
3. To achieve grade A on paper 1 candidates had to score 66 marks out of 100. What mark on paper 2 gives equal proportions of candidates achieving grade A on the two papers? What is this proportion?
4. The candidates' marks for the two papers could also be illustrated by means of a pair of box-and whisker plots. Give two brief comments comparing the usefulness of cumulative frequency graphs and box-and-whisker plots for representing the data.

\includegraphics{figure_3} The birth weights of random samples of 900 babies born in country \(A\) and 900 babies born in country \(B\) are illustrated in the cumulative frequency graphs. Use suitable data from these graphs to compare the central tendency and spread of the birth weights of the two sets of babies. [6]

Paul drew a cumulative frequency graph showing information about the numbers of people in various age-groups in a certain region X. He forgot to include the scale on the cumulative frequency axis, as shown below. \includegraphics{figure_12}

1. Find an estimate of the median age of the population of region X. [1]
2. Find an estimate of the proportion of people aged over 60 in region X. [2]

Sonika drew similar cumulative graphs for another two regions, Y and Z, but she included the scales on the cumulative frequency axes, as shown below. \includegraphics{figure_12b}

1. Find an age group, of width 20 years, in which region Z has approximately 3 times as many people as region Y. [1]
2. State one advantage and one disadvantage of using Sonika's two diagrams to compare the populations in Regions Y and Z. [2]
3. Without calculation state, with a reason, which of regions Y or Z has the greater proportion of people aged under 40. [1]