Lite GCSE Maths Cumulative Frequency Mark Scheme Name: Class: Author: Date: Time: 29 Marks: 27 Comments: Page 1 of 7
. (a) Evidence that line at 90 drawn or used Line from 40 days drawn or used 40-41 days 87-89 patients False as just over 40 or just about true as nearly 40 Must make a conclusion and refer to values False as 88 < 90 or just about true as 88 nearly 90 (b) Range marked from 1 to 8 Median and quartiles marked at 4.1, 5, 5.8 Box formed and whiskers correctly joined (c) 80 746 ( any value in table) 9 37 5 4 21 4 All values ± 1 Award A0 if total is not 80 A2 [9] M2. (a) (34 to 35) (17 to 18) Follow through No working accept 16 to 18 ft (b) 80 36 or 80 35 visits will cost Sight of 44 or 45 22 or 22.50 2200 A0 ft [4] Page 2 of 7
M3. (a) (i) 100 (ii) 106 93 93 106 Reading from graph = 13 (b) (i) George, lower interquartile range Accept smaller range/smaller spread oe (ii) Brian, lower median oe (B0 Brian 70, George 85) [5] M4. (a) correct midpoints correct frequency 1 12, 3 18, 5 10,... allow one error their (midpoints frequency) their(1 12) + their(3 18) + their (5 10) +... (their 190) 50 3.8 or 3 SC These values with full method: 4.8 (using ucb as midpoints) or 2.8 (using lcb as midpoints) or 4.3 (using 1.5, 3.5, 5.5,... as midpoints) or 3.3 (using 0.5, 2.5, 4.5,... as midpoints) (b) (i) 3.4 to 3.5 (ii) UQ LQ or attempt to find both UQ and LQ with either correct and their (UQ LQ) or distances at CF 12.5 and 37.5 marked on graph and their (UQ LQ) seen 3.3 to 3.6 [7] Page 3 of 7
M5. Reading from graph at LQ and UQ Accept any indication 19 11 = 8 for example Can read from 10.25 and 30.75 11 (mins) and 19 (mins) Either order.(10.25 gives 11.125, 30.75 gives 19.5). Reading from graph 1 mm tolerance rule applies. [2] Page 4 of 7
E1. This question is drawn from our specimen paper produced in advance of live examinations. As such, the question was not used in a live examination and therefore no Examiner's Remarks exist. E2. In part (a) with the cumulative frequency diagram drawn this enabled a good number of candidates to correctly obtain the interquartile range. There were a few who simply worked on the Lower Quartile which gained no credit in isolation. For part (b) a good number of correct answers were seen but quite a number failed to subtract their read off value from 80 to give the number above 24 minutes and instead had the figures the wrong way around. Quite a few candidates simply worked out 80 times 50 p and surprisingly for this level some candidates lost marks for incorrect money notation e.g., 2200 or 22.5 E3. Intermediate Tier Many got part (a)(i) correct with a common error being 95 from the middle of 70 to 120. Part (a) (ii) was often done with no lines on the diagram so that no method marks could be awarded if the answer was wrong. Many got part (b)(i) correct but often referred to Brian s lower scores in part (b)(ii). Higher Tier Almost every candidate scored full marks on part (a). The only errors were misreads or calculating the values for George. Part (b) was less successful. Candidates write lines of nonsense to justify an answer instead of giving a response in statistical terms. E4. Many candidates showed no appreciation of any of the routines involved in this question. In part (a) those candidates who managed to produce a correct method for estimating the mean invariably scored 3 marks only, because they could not handle 190 50 correctly with 3 remainder 40 often becoming 3.4. Some candidates managed to show the method to get to 190 but did not always do this accurately because of multiplication and addition errors. Others knew the routine but used the wrong midpoints, usually the upper class boundaries. A large number of candidates either added the frequencies, the cumulative frequencies or the midpoints; dividing by 5 instead of 50 was another common error. In part (b) the median was often correct but there was less success with the interquartile range. Candidates who knew what to do often lost marks because of misread scales or inaccurate drawing. In their method for the interquartile range, some candidates put their quartiles in the wrong position, for example at 10 and 40, others added the quartiles and some simply gave the lower quartile. A common error was to work from the horizontal axis to the vertical for both the median and the quartiles. Page 5 of 7
E5. Higher Tier This was well done by the majority of candidates. A common error was to misread the scales as 12 and 18. A minority read from 10.25 and 30.75. Intermediate Tier Another poorly answered question. Most candidates failed to relate the middle 50% with the interquartile range and simply opted for 50% being at 20 on the cumulative frequency axis. Of those who did realise that quartiles were involved quite a few misread the horizontal scale giving answers of 12 and 18. Page 6 of 7
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