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1 Guidance on the use of codes for this mark scheme M A C P cao oe ft Method mark Accuracy mark Working mark Communication mark Process, proof or justification mark Correct answer only Or equivalent Follow through arpercollinspulishers Ltd 01 1

2 Question Working Answer Mark AO Notes Grade 1 a = would vote for Party A. This is over 0% of voters so Party A should e confident of winning = 1 1 students are in the sample. A1 for multiplication of total population y proportion of sample for for explanation that this represents over half the whole population and so a majority is likely for multiplication of total population y proportion of sample A1 cao At four different points in the concert, entrances or ars, each point to conduct the survey on approximately 100 people each, trying to ask as many males as females. for explanation of general method of sampling for specific example related to the concert crowd arpercollinspulishers Ltd 01

3 4 a Define what she means y a good train service. Could e numer of trains per hour, or numer of trains that are on time in a specified period, or customer satisfaction regarding the quality of various aspects of the journey such as level of cleanliness, availaility of sets etc. To find out if the statement is true or not, the first step is to see what has changed since the aunt has een travelling (see aove). for explanation of sujective nature of this enquiry for description of what might e seen as good Data to e collected would depend on what the aunt felt had changed (or what has actually changed).this could e data from the train company aout volume of trains, amount of rolling stock at one time, numer of complaints received and aout what. This could also e data collected from a customer survey. owever, this would e real time and would e hard to gather retrospectively as it would e sujective and may not e possile, depending on time frame. for explanation of possile data to e collected with reason for appreciation of this eing a sujective enquiry over time for a correct description of a data-collection process. 0 = 0 So there were 0 eggs in total.0 = 0 1 = 4 = 8 1 = = 16 eggs 0 16 = 4 eggs to find. ens could lay or 4 eggs. ( 6) + (4 4) = = 4 ( ) + (4 7) = = 4 Eggs (E) Frequency (f) E f Eggs (E) Frequency (f) E f Could e eggs, frequency 6 and 4 eggs, frequency 4. for total eggs (0) for multiplication of eggs y frequency plus addition and sutraction to find how many eggs are left to find oe for one solution Could e eggs, frequency and 4 eggs, frequency 7. for a second solution for clear description or tale oe arpercollinspulishers Ltd 01

4 6 a = patients.1 for addition of frequencies Total numer of minutes = sum of (midpoint frequency) for each class = 74 Mean time = 74 = minutes Time (minutes) Midpoint (M) Frequency (f) for midpoints frequencies for total minutes for division of total minutes y total patients (ft) M f c d Estimated mean = minutes Modal time = 1 0 minutes ( 79 1) = 40 The median is the 40th person. The 40th person is in the 1 40 group. Median time is 1 40 minutes For the group who waited over one hour (61 70), there were patients. So 74 patients were seen in one hour or less = So 9.7% of patients saw a doctor within one hour. Time (minutes) Midpoint (M) Frequency 1 9 (f) M f Estimate mean waiting time = minutes The hospital would use the modal time. 9.7% of patients saw a doctor within one hour. 1 A1 10 for appropriate rounding to whole minutes for mode for median 1 for correct, shortest, average waiting time for calculation of or 1 ( ) as a percentage 79 A1 cao arpercollinspulishers Ltd 01 4

5 7 a No. It only shows proportions P1 for reference to proportions Estimate: Often: 90 (= %) Very often: 7 ( 0%) Rarely: 100 ( 0%) Never: 7 ( 0%) Always: 10 ( %) Summary and interpretation of availale information and data 8 The minutes spent waiting is halfway etween the 4-minute and the 6-minute groups. These people are in that and, ut maye no one had to wait exactly minutes. 9 Divide the frequency of the class interval y the width of the class interval to find the frequency density. 10 Kathy s mean (scores in order): ( ) 7 =.7 Connie s mean (scores in order): ( ) =.6 Evie s mean (scores in order): ( ) = 4.4 Kathy would choose her mean score of.7. Connie would choose her median score of 7. Evie would choose her modal score of 8. C 4 for commenting on the proportions of people giving the range of answers, for example: All percentages are estimates ased on the approximate angle of the sector of the pie chart. % of people sampled said that they often considered their health when planning a diet, with % saying that this was always the case and 0% saying very often. 0% rarely consider their health when planning a diet and 0% never do. C for summary, for example: So approximately half the sample consider their health to some degree and half do not. for awareness that the minutes represents the midpoint of a class of grouped data, so people may have een waiting for any time etween 4 and 6 minutes 1 for correct method for calculation of frequency density 1 1 for calculation of all three means for identification of all three modes for identification of all three medians 1 for correct average identified in all three cases M Dancer Scores Mean Median Mode Kathy 8, 7, 6,.7,,, 4 Connie 9, 8, 7,.6 7, Evie 8, 8,,, arpercollinspulishers Ltd 01

6 11 Working in thousands of pounds: RangeA = = 70 Range = 4 = MeanA = ( 86 6 ( 18)) = 1. Mean = ( 4 6 ( 4 6) ( )) = Valid advice ased on the salary scales provided (see notes), for example: Jasmin should join firm if she is prepared to accept that the highest salary is not as high as that offered y firm A. owever, the starting salary is higher and Jasmin can progress more quickly to a higher salary with firm than with firm A. There is a greater range of salaries in firm A than in firm. Jasmin should join firm A if she aspires to eing the oss! Alternatively she could start with firm and move to firm A after 7 salary increments for maximum earnings. P1 6 Firm Range Mean Median Mode A for calculation of ranges for calculation of means for identification of medians for identification of modes P1 for justification of either firm A or firm for use of tale oe for comparison M arpercollinspulishers Ltd 01 6

7 1 a Set of grouped data with an estimated range of 6. for correct example (class widths do not need to e equal), e.g. 0 x < ; x <; x < Estimated range (from midpoints) = 8.. M Set of grouped data an estimated median of 46. for correct example (class widths do not need to e equal), e.g. Class 0 x < 4 4 x < x < 0 Midpoint 46 Frequency 1 cf 6 11 n = 11 hence the sixth data point is the median Estimated median (from midpoint) = 46 c Set of grouped data an estimated median of. and an estimated range of 6 for correct example of estimated median for correct example of estimated range (class widths do not need to e equal), e.g. Class 0 < 0 0 x < x < 119 Midpoint Frequency 1 cf 6 11 n =11 hence the sixth data point is the median Estimated median (from midpoint) =. Estimated range (from midpoints) = 7 10 = 6 d Set of grouped data an estimated mean of 6 (to one decimal place). 6 for correct division: (sum of frequencies midpoint ) (total frequency) for correct example of estimated mean (ft) (class widths do not need to e equal), e.g. Class Frequency (f) Midpoint (m) f m 0 x < x < x < x < x < x < Totals Estimated mean= arpercollinspulishers Ltd 01 7

8 1 Median = n 1 Lower quartile = th value n 1 4 th value (n + 1) Upper quartile = th value So if you have a tale with 1 values these will e the 6th, rd and 9th values. Order Value 1 for correct formula for median for correct formula for LQ for correct formula for UQ, for values for UQ and LQ with a difference of 7 for explanation of difference in relation to range in this context M Difference etween 14 and 7 equals 7 as required These can e adapted as long as rows are added equally in each section (see example elow). Order Value Difference etween 14 and 7 equals 7 as required. arpercollinspulishers Ltd 01 8

9 Either arold, as he had igger tomatoes, or Connie, as she had more tomatoes (depending on if you want lots of tomatoes or large tomatoes!). P1 P1 for choice of one person with justification for further consideration of second person M 1 a The statement: There is strong evidence to support my hypothesis is more precise. In reality it is usually not possile to prove a hypothesis just to gather evidence to support it. P1 P1 for selection of There is strong evidence to support my hypothesis with explanation aout practicalities of proving an hypothesis M i ii ecause you may not have gathered enough evidence. ecause you haven t gathered enough evidence or you re using a null hypothesis. 16 a Valid comparative statement such as: The means are very similar ut there is evidence that the roadsheets use a roader range of length of words. for explanation of having sufficiently large sample / evidence for giving same reason / an awareness of the practical difficulties of getting all other variales equal or unchanged so that they do not affect the success or otherwise of your evidence gathering. oe for comparative statement oe arpercollinspulishers Ltd 01 9

10 c No, it provides some evidence, ut only assuming length of words is a suitale measure of difficulty. The length of words may not e the thing that readers find makes a paper hard to read. For example: ow long did it take to read the sample or a specific question to challenge the readers understanding of the sample. Could also look at the modal word length to see if there is evidence to support the roadsheet using a greater range of words, for example: Are most of the words in the taloid four letters long? for explanation that this is insufficient evidence to answer the question oe for a suitale further question oe 17 Mean1 = 4 40 = 11.7 There is a difference of 0.6 so mean is 11.7 ± 0.6. So it is either 1 or The new total is either: 40 1 = 480 (increase of ) or = 40 (decrease of ) y trial and improvement: 1 and 10 are reversed. The 1 and the 10 are the wrong way round. Mas 0 < m < m 10 < m 1 < m 0 < m Total s s freq mp m f freq m f for calculation of new mean for calculation of new totals for trial and improvement with information gathered oe 1 1 for correct identification of 1 and 10 for tale to show corrected data oe arpercollinspulishers Ltd 01 10

11 18 a The diagram chosen needs to show how the mass of each cheese varies from one year to the next. A line graph, as follows, is a good choice when there is variation over time. Mean Median Mode Range W RC P1 P1 for report that includes an awareness of change over time, and which cheeses are increasing and which are decreasing in popularity for appropriate diagram or graph oe for calculation of ranges to show which cheeses are most popular oe for calculation of mean or median to show average mass of cheese purchased oe for interpretation of calculations within the report WC RL S E arpercollinspulishers Ltd 01 11

12 19 Students diagrams, measures and reports will vary. Mean Median Mode Range C PG.8 4 S 4.6 M S 4 4, for report that includes an awareness of change over time and which wines are increasing and which are decreasing in popularity for appropriate diagram / graph oe for calculation of ranges to show which wines are most popular oe. for calculation of mean, median or mode to show average numer of cases of wine purchased purchased oe CS R 0 for interpretation of calculations within the report 0 Estimated mean = = 7.6 minutes From the cumulative frequency (cf) graph (some variance depending on students reading of unmarked intervals on graph): mp c.freq freq f mp Totals Estimate: 8 minutes (to the nearest minute). A1 4 for identification of frequencies from cf graph for identification of mid-points of classes from cf graph for tale to show data derived from cf graph oe A1 for their estimated mean (ft) Allow range of 6 9 minutes 1 Find the top 1% on the cumulative frequency scale, read along to the graph and read down to the marks. The mark seen will e the minimum mark needed for this top grade. for explanation of use of graph for explanation of where to find the minimum grade arpercollinspulishers Ltd 01 1

13 Class width fd f A1 A1 for identification of class widths and frequency densities for calculation of frequencies using f = fd w for clear tale showing w, fd and f Frequency density (fd) = frequency (f) divided y class width Numer of students getting top grade is 10% of 1 = students got = Class width = 0 0 ( ) =.667 Mark for top grade = The mark for the top grade is 8.7 (or 86 to the nearest integer score). for division to get oe for class width oe cao 6 Work out frequency density from frequency = frequency class width for calculation of frequency of 0 for class travelling over 4 km to church Class fd f width people travel more than 4 km to church = 4 = 0.147= 0.1 to dp The proaility is 0.1 (or 4 ). A1 4 for 0 16 oe for rounding to one dp A1 cao Notes: Any one in 4 6 class could travel exactly 4 km to church so only consider the 8 10 class arpercollinspulishers Ltd 01 1

14 4 C Max Min 4 LQ 6 4 M 7 UQ 9 8 R 6 1 IQR 4 Gariel could see either doctor, ut students should provide a plausile reason, for example, Dr all ecause patients never have to wait longer than 10 minutes, whereas they may have to wait up to 14 minutes for Dr Charlton; or Dr Charlton ecause the average waiting time is less than for Dr all. for interpretation of data from ox plots for choice of doctor with reason, e.g. average waiting time oe for choice of doctor with further reason, e.g. reference to range or inter-quartile range G Max 9 9 Min 1 LQ 40 0 M 6 UQ 6 7 R IQR There are quite a few possile correct answers, for example, oys results have higher median and higher quartiles; or girls got lower marks than the oys, interquartile range is same for oys and girls. for interpretation of data from ox plots for choice of either oys of girls with one justification, using their data from ox plots oe for choice of either oys of girls with one further justification, using their data from ox plots oe 6 Many different possiilities. Each should contain no specific data only general data such as: Scarorough generally had more sunshine than lackpool, lackpool tended to have more settled weather than Scarorough or Scarorough had more sunshine on any one day. for first correct comparison etween Scarorough and lackpool for a further correct comparison etween Scarorough and lackpool 7 ox CF Max Min 10 0 LQ 0 8 M 4 61 UQ 4 66 R IQR 1 8 These are representations from different distriutions as no data points match for measures of spread or tendency. P1 for interpretation of data from ox plots P1 for comparison of measures of spread or tendency to arrive at a no answer 8 The measures of central tendency are likely to e different. The range is likely to e igger for 7 to 1 than for 1 to 1 only. The greatest value (for the tallest student) will e the same and there may e similar differences etween oys and girls. for mention of comparisons of range of heights oe for consideration of gender differences in height with comparison of different age ranges, for example, girls are often taller than oys in Y7 and this trend is reversed y the time they reach Y1 arpercollinspulishers Ltd 01 14

15 9 a Suitale statements aout the distriutions with justification for why the representations are from different distriutions. for comparison statements such as D1 has data for ages 18 11, which D does not; D has data for ages 0, which D1 does not; D1 has a positive skew so it has a low mode with a long right tail and D has a slight negative skew, so it has a higher mode ut more consistency across a greater range oe Distriution 1 is for Africa, distriution is for Europe, plus oservations such as: there is a peak at 1; distriution 1 is positively skewed; there is a more constant frequency across the range for distriution with more women marrying older in distriution. for oservation of skewness and students comments on and perception of possile reasons such as: women in Africa tend to marry at a younger age; European women have etter health care or careers and so marry later; there is more gender equality and independent women in Europe oe 0 a Examples such as: positive skew income distriution negative skew age at death in developed countries. for positive skew context where there is a long tail to the right (higher values) and the ulk of the distriution is to the left (lower values) for negative skew context where there is a long tail to the left (lower values) and the ulk of the distriution is to the right (higher values) The ox will e shifted to e in line with the ulk of the distriution. It will veer right for negative skew, left for positive and central for no skew. for description of negative skew that includes a comment on the distriution eing focused to the right (lower values) oe c Suitale ox plot for each distriution for suitale positive skew ox plot 1 for suitale no skew ox plot 1 for suitale negative skew ox plot Positive skew (long right tail, median to the left) 6 arpercollinspulishers Ltd 01 1

16 1 a Examples of diagrams to illustrate changes over a ten-year period could either e numer of flights or numer of passengers as line graphs oe. Students research may vary, as will their diagrams. Examples of diagrams to show changes over the period 1980, 1990, 000 could e either numers of flights or numers of passengers as line graphs oe. for graph or diagram to illustrate either flights or passengers from 1980 to1990 oe for clear diagram and appropriate laels for graph or diagram to illustrate either flights or passengers from 1980 to 000 oe for clear diagram and appropriate laels for appropriate research for their extrapolation figure for numer of passengers in 010 for their extrapolation figure for numer of flights in 010 c Extrapolating the data in the tale for the period etween 1980 and 1990 gives: Passengers in 010 approximately 14 (million) Flights in 010 approximately 1400 (thousand) or 1.4 million. owever, looking at current data on the internet, the aove 010 estimates were already eing approached in 000 (cheap flights were introduced). Extrapolating the later data (up to 1999) gives: Passengers in 010 approximately 00 (million) arpercollinspulishers Ltd 01 16

17 Flights in 010 approximately 000 (thousand) or.0 million. 7 a P1 P1 for appropriate distance time graph c 1 km 86 minutes A1 A1 A1 for ft answer from their graph A1 for ft answer from their graph arpercollinspulishers Ltd 01 17

18 a arry may have misinterpreted the information ecause owning multiple TVs is more likely to e a measure of wealth rather than of health. In countries of high wealth, where people are likely to own more than one TV, the healthcare system is proaly much etter than in poorer countries, or nutrition is etter than in poorer countries. It may also e a measure of accessiility to electricity. P1 P1 for clear evidence of awareness of other variales that could contriute to the results shown on the scatter graph A more likely explanation for the relationship is that people who live in a more affluent country will have more access to high-value goods, such as TVs, a etter supply of electricity and etter healthcare and nutrition. for appropriate suggestions as descried arpercollinspulishers Ltd 01 18