A-LevelMathematicsProbability and statistics9709/62 · Feb/Mar 2018 · Q14 Marks

There are 900 students in a certain year-group. An identical puzzle is given to each student and the time taken, t minutes, to complete the puzzle is recorded. These times are summarised in the following frequency table. Time taken, t minutes t≤3 3<t≤4 4<t≤5 5<t≤6 6<t≤8 8 <t≤ 10 10 < t < 14 Frequency 120 180 200 160 110 80 50 On the grid, draw a cumulative frequency graph to represent the data. Use your graph to estimate the median time taken by these students to complete the puzzle. [Figure 1.1]

On the grid, draw a cumulative frequency graph to represent the data. Use your graph to estimate the median time taken by these students to complete the puzzle.[4]

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Mark scheme

Marking points from the official mark scheme (Feb/Mar 2018). The mark or mark type is shown in brackets.

[M1] Attempt to plot cumulative frequencies at ucb and all points joined between (3,y1) and (14,y2). Cf table not required.
[A1] Linear scales starting at (0,0) and axes labelled cf and time in mins, all points correct; (allow straight lines or curves)
[M1] 450 seen in median attempt on increasing CF graph (independent);
[A1 FT] Correct (4.7 < m < 4.9) or FT from reading their increasing graph at cf = 450

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