Compare using diagrams only

3 The following cumulative frequency table shows the examination marks for 300 candidates in country \(A\) and 300 candidates in country \(B\).

1. Without drawing a graph, show that the median for country \(B\) is higher than the median for country \(A\).
2. Find the number of candidates in country \(A\) who scored between 20 and 34 marks inclusive.
3. Calculate an estimate of the mean mark for candidates in country \(A\).

4 The Mathematics and English A-level marks of 1400 pupils all taking the same examinations are shown in the cumulative frequency graphs below. Both examinations are marked out of 100 .
\includegraphics[max width=\textwidth, alt={}, center]{be6c6525-a20c-42d0-8fef-1cd254baaa76-06_1682_1246_404_445} Use suitable data from these graphs to compare the central tendency and spread of the marks in Mathematics and English.

5. (a) Explain briefly the advantages and disadvantages of using the quartiles to summarise a set of data.
(b) Describe the main features and uses of a box plot. The distances, in kilometres, travelled to school by the teachers in two schools, \(A\) and \(B\), in the same town were recorded. The data for School \(A\) are summarised in Diagram 1. \section*{Diagram 1} For School \(B\), the least distance travelled was 3 km and the longest distance travelled was 55 km . The three quartiles were 17, 24 and 31 respectively. An outlier is an observation that falls either \(1.5 \times\) (interquartile range) above the upper quartile or \(1.5 \times\) (interquartile range) below the lower quartile.
(c) Draw a box plot for School B.
(d) Compare and contrast the two box plots.
(4)