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Edexcel GCSE

Statistics 1389

Summer 2006

Mark Scheme

Edexcel GCSE

Statistics 1389

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Summer 2006

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__Contents__

1Notes on Marking Principles 2 – 3 2Paper 1389/1F Mark Scheme 4 – 11 3Paper 1389/1H Mark Scheme 12 – 22

**
NOTES ON MARKING PRINCIPLES**

**1** **Types of mark**

- M marks: method marks
- A marks: accuracy marks

- B marks: unconditional
accuracy marks (independent of M marks)

**2** **Abbreviations**

cao – correct answer only

ft – follow through

isw – ignore subsequent working

SC: special case

oe – or equivalent (and appropriate)

dep – dependent

indep
- independent

**3** **No working**

If no working is shown then correct answers normally score full marks

If no working is shown then
incorrect (even though nearly correct) answers score no marks.

**4** **With working**

If there is a wrong answer indicated on the answer line always check the working in the body of the script (and on any diagrams), and award any marks appropriate from the mark scheme.

If it is clear from the working that the ��correct�� answer has been obtained from incorrect working, award 0 marks. Send the response to review, and discuss each of these situations with your Team Leader.

Any case of suspected misread loses A (and B) marks on that part, but can gain the M marks. Discuss each of these situations with your Team Leader.

If working is crossed out and still legible, then it should be given any appropriate marks, as long as it has not been replaced by alternative work.

If there is a choice of methods shown, then no marks should be awarded, unless the answer on the answer line makes clear the method that has been used.

If there is no answer on the
answer line then check the working for an obvious answer.

**5** **Follow through marks**

Follow through marks which involve a single stage calculation can be awarded without working since you can check the answer yourself, but if ambiguous do not award.

Follow through marks which
involve more than one stage of calculation can only be awarded on sight
of the relevant working, even if it appears obvious that there is only
one way you could get the answer given.

**6** **Ignoring subsequent
work**

It is appropriate to ignore subsequent work when the additional work does not change the answer in a way that is inappropriate for the question: eg. incorrect cancelling of a fraction that would otherwise be correct

It is not appropriate to ignore subsequent work when the additional work essentially makes the answer incorrect eg algebra.

Transcription errors occur
when candidates present a correct answer in working, and write it incorrectly
on the answer line; mark the correct answer.

**7** **Probability**

Probability answers must be given a fractions, percentages or decimals. If a candidate gives a decimal equivalent to a probability, this should be written to at least 2 decimal places (unless tenths).

Incorrect notation should lose the accuracy marks, but be awarded any implied method marks.

If a probability answer is given on the answer line using both incorrect and correct notation, award the marks.

If a probability fraction
is given then cancelled incorrectly, ignore the incorrectly cancelled
answer.

**8** **Linear equations**

Full marks can be gained if
the solution alone is given on the answer line, or otherwise unambiguously
indicated in working (without contradiction elsewhere). Where
the correct solution only is shown substituted, but not identified as
the solution, the accuracy mark is lost but any method marks can be
awarded.

**9 Parts of questions**

Unless allowed by the mark
scheme, the marks allocated to one part of the question CANNOT be awarded
in another.

1F Section ANoWorkingAnswerMarkNotes1

3 B3 cao (B1 for each correct tick. For 4 ticks in the table-

deductone mark from the total number of correct ticks)SC: B1 for 5 ticks

2 (a) Stranraer - Belfast 1 B1 cao (b) 4 1 B1 cao (c) It is the longest route. It takes twice as long as the second longest route, etc Other factors may include the cost, the number of ferries on each route, the ease of getting to the port, competition from other ferries, etc

2 B2 for two sensible reasons

(B1 for one sensible reason)

3 (a) 440, 410, 850 200, 420, 230

2 B1 for 440, 410 and 850

B1 for 200, 420 and 230

SC: B1 for 4 correct numbers out of 6)

(b)(i) 2 B1 for = oe ( 0.235 or 23.5% awrt)

(ii) B1 for = oe (0.247 or 24.7% awrt)

1F Section ANoWorkingAnswerMarkNotes(c) Free-range hens lay larger eggs then battery hens

Battery hens lay more small eggs

Both types of hens lay similar number of medium eggs.

Free range eggs lay more eggs overall

(Figures are acceptable)

2 B2 for two sensible reasons (B1 for one sensible reason)

4 (a) 22.81 or 22810

1 B1 (b) Rounding errors

1 B1 (c) (i) Falling or going down or decreasing

(ii) Level or flat or stays the same or up or down (by small amounts) or not much of a trend oe

2 B1, B1 5 (a)

1 B1 for shading 4 squares correctly (b) Uneven spread 1 B1 for ��uneven spread�� or ��bunched together�� (oe) 6 (a) 3 1 B1 cao (b) 2+3+4+5+7+8+10+11 50 1 B1 cao (c) ��positive�� or ��more sent more received�� 1 B1 for ��positive�� seen or ��more sent more received�� oe (d) Line of best fit 1 B1 for a line close to the points (e) 6 1 B1 for 5, 6 or 7

1F Section ANoWorkingAnswerMarkNotes7 (a) 8, 3 and 520, 210 26, 1560

1 B1 for completing the table accurately (b)

602 M1 for any ��figure divided�� by 26 A1

(c) for any one of more data, mode or modal size/weight range, IQR, SD, frequency/ number of outlier

1 B1

1F Section BNoWorkingAnswerMarkNotes1 (a) for any two of ��cheaper�� or ��less time consuming�� or ��less data to consider�� or ��it is easier to do�� oe

2 B2 for any correct 2 (B1 for any one)

(b) A suitable closed question

With boxes or answers to choose from or options within the questions

2 B1 B1

(c)(i) (ii)

Identify problems shows likely answers

check the questions work

checks the questions are clear,

give an idea of response rate

checks the time it takes to do

2 B2 for any two sensible reasons (B1 for one)

(d) Not suitably worded question

Plus any one from:

It asks two questions

Needs response boxes/options

It is a leading question

It puts pressure on respondent to agree

It is biased

(Any other valid point acceptable)

2 B1 B1

1F Section BNoWorkingAnswerMarkNotes2 (a) Label B A C on probability scale 2 B2 for plotting points: 0 < B < 0.25; A within 0.5cm of 0.5; C at 1 (B1 for any two correct)

(b) 1 – ( 0.5 + 0.25 + 0.15 ) 0.1

2 B2 cao (B1 for 0.9 seen) (c) 0.15 + 0.25 0.4

1 B1 cao (d) 3

1 B1 cao (e) 0.5 0.5 0.25

2 M1 for 0.5 0.5 A1 for 0.25 oe

3 (a)(i) 40

3 B1 cao (ii) 34.5

B1 for (iii) Whole number in range 27 – 32 inclusive

B1 for 27; 28; 29; 30; 31; 32 (b) 4 | �� 3 3 5 8 8 5 | �� 1 2 3 5

2 B2 cao (B1 for both 4 | ��

3and 5 | ��1)(c)(i) 39 2 B1 ft stem and leaf diagram if 8 or 9 values added (ii) 19 B1 ft stem and leaf diagram if 8 or 9 values added

(d) The female students read the essay more quickly; The median time for the female students is less than the median time for the male students;

More of the female students read the essay in less than 38 minutes.

2 B1 for ��females quicker�� oe

B1 for a sensible reason that compares like with like

1F Section BNoWorkingAnswerMarkNotes4 (a) A list of (all) the plants (in the greenhouse)

1 B1 cao (b) Number the plants. Use random numbers. 2 B1 for ��number the plants�� oe B1 for ��use random numbers�� oe

(c) Vertical lines with height 10, 4, 1 2 B2 cao (B1 for any two correct)

(d) 3 1 B1 cao (e) 1 5 + 2 7 + �� 70 2 M1 for 1 5 + 2 7 �� A1 cao

(f) ��70�� 100 7000 1 B1 ft ��70�� 100 from (e) 5 (a)(i) , etc 30, 32, 34 4 B2 for 30, 32, 34

(B1 for one or two of 30, 32, 34)

(ii) Moving averages plotted at (2, 25), (3, 27), (1, 28), (2, 29), (3, 30), (1, 32), (2, 34)

B2 cao

(B1 ft for 4 points plotted correctly 2mm)

(b) (Sales are) increasing 1 B1 for ��increasing�� or ��going up�� (oe) (c)(i) 3 or Sep – Dec 2 B1 for 3 or ��Sep – Dec�� oe (ii) Reason B1 for ��(increased sales due to) Christmas�� (oe) (d) 116 2 B2 for 116 (B1 for or or 16% or 1.16 or 0.16 or or )

(e) 100 – 5 100 95

2 B1 cao B1 cao

1F Section BNoWorkingAnswerMarkNotes6 (a)(i) 95 – 45 = 50

2 B1 cao (ii) 70 – 55 = 15

B1 cao (b) ��affected by extreme values�� or ��not all values used��

1 B1 for ��affected by extreme values�� oe or ��not all values used�� oe (c) Box plot drawn

2 B2 cao (B1 for box plot with only one error)

(d) ��Some (25%) of the cars were speeding��

��A car traveled at 25 mph above the speed limit��

��100 cars were speeding��

2 B1 for a suitable comment B1 for a numerical justification

1H Section ANoWorkingAnswerMarkNotes## 1

## (a)

8, 3 and 520, 210. 26, 15601 B1 (b)

=Any figure divided by 26

602 M1 A1

## (c)

ANY ONE FROM:

More data.

Mode or Modal size/weight

Range

Minimum size

Inter quartile range

Standard Deviation(any sensible answer)

Frequency/Number of outliers1 B1 2 ## (a)

## 440, 410, 850

200, 420, 230

2 B1 B1

(b)(i)

## (ii)

(o.e) ( 0.235 or 23.5% awrt)(o.e.) (

0.247 or 24.7%awrt)2 B1

B1

(c) ANY TWO FROM:

Free-range hens lay more large eggsthan battery hens.

Battery henslaymore smalleggs.

Both types of henslaysimilar numbers of mediumeggs. (any 2 different sensible statements)

Free range hens lay more eggs overallFigures acceptable as long as showing a comparison

Ignore incorrect statements

Accept Opposites2 B1

B1

1H Section ANoWorkingAnswerMarkNotes

## 3

## (a)

1/3 o.e.1 B1 (b)

1 : 2 or one to two1 B1

## (c)

21 B1 4

## (a)

Every/eachitem in the population hasanequal chanceof selection.1 B1

## (b)

Either: 10, 07, 30, 39, 05, 37, 26, 04, 13, 48

OR: 10, 07, 30, 39, 05, 07, 37, 26, 04, 13Allow with or without leading 0��s

2 B1 B1 (B1 if 1 wrong)

(c) Number classChoose those

corresponding to random numbers2 B1 B1

5 (a) 22.81allow 228101 B1 (b) Roundingerrors1 B1 (c)(i) (ii)

Fallingorgoing downordecreasing

LevelorFlator��Stays the Same��orup and down by small amounts.(oe)(must be small or equivalent word)2 B1 B1

6 (a) There are more DVD��s sold.

Size of DVD pie chart > Size of video pie chart.2 B1 B1

(b) ANY ONE FROM: The

ratio(% or proportion) of videos to DVD��s was similar(about the same) in all the shops.The

% of allDVDs sold wasgreaterthan the % of videos sold in shops C, D and E.The

% of allVideos sold wasgreaterthan the % of DVDs sold in shops A and B.All may be implied.

Do not allow comparisons within single shops.

1

B1

1H Section ANoWorkingAnswerMarkNotes7 (a)

122, 107.(SC 122.2 awrt 106.6 awrt gets B1)

2 B1 B1 (b) 25% (not 1/4 or 0.25)1 B1 (c) M1 for 5 ^{th}root of product oftheirnumbers

118(awrt from correct working)2 M1 A1

(d) Average rate of increase 18% (18.4 acceptable)1 B1ft (e) Level trend until 2005 (allow dip in2003 and/or drops at 2005)

No trend

Fluctuating

No real pattern

Uneven

NOT varies1 B1 8 (a) 1400 or 1600 tonne1 B1 (b)

ANY ONE FROM: The

meanwould be best.

1 standard deviation more than the mean.Any

figure between 1000 and 1200.(An actual figure between these is acceptable.)

ANY ONE FROM:

The

maximumquantity is likely to bewasteful.The

maximumquantity will buildup too much stock.The

mean or a little moreshouldcover the needs over time.

To avoid shortfall or build up of stock.(Any reasonable comment to back up the first B1 is acceptable)

(SC B2 for a little below the mean (approx 950) to save waste of money or overstocking.

2 B1

B1

1H Section BNoWorkingAnswerMarkNotes1 (a)

7, 4, 5, 2, 6, 3, 1.

0, 4, 0, 4, 9, 1, 0.

Reverse order

1, 4, 3, 6, 2, 5, 7 gives B0

36, 4, 4. 4, 1, 9, 36 SC B12

B1 B1ft

(b) = 18,

= 1 – 0.3214

(reverse ranks give d^{2}= 94)

=0.679CAO consistent with ranking.

(- value is from reverse working)

2

M1A1

(c) There is some positivecorrelation (or association/agreement o.e.). CAOEITHER:

Thehigher the HDI the higher the GNP.OR:

Thelower the HDI the lower the GNP

(Accept wealth and Quality of life)2 B1

B1

1H Section BNoWorkingAnswerMarkNotes2 (a)(i)

(ii)

ANY TWO FROM: It is

cheaperIt is

less timeThere

is less data to be considered.It is

easierto doOr reverse

Any correct 2 ignore incorrect

2

B1B1

(b) Quota1 B1 (c) Any suitable closedquestionWith boxes or answers to choose from or options within the question.

2 B1 B1

(d)(i)

(ii)

ANY TWO FROM: It

identifies problemsin answering questions.It

shows likely answers(or other suitable)It

checks the questions work.It

checks the questions are clear.

Gives an idea of responserate.

Checks time it takes to do.2 B1 B1 (e) NOT/NOa suitably worded question.PLUS ANY ONE FROM:

It

asks two questions.

Needs response boxes/options.It is a

leadingquestion.It

puts pressure on respondentto agree.It is

biased.(Any other valid point acceptable.)

2 B1 B1

1H Section BNoWorkingAnswerMarkNotes3 (a)(i)

(ii)

Table shows figures you might see

6.7 (allow 6700)

3.6(AWRT)

196 7.3 68.89 16 2.7 2.89 4 4.7 13.69 36 0.7 0.09 64 1.3 5.29 4 4.7 13.69 36 0.7 0.09 81 2.3 10.89 4 4.7 13.69 16 2.7 2.89 457 132.1 3

B1

M1 A1

(b) Manufacturing lost fewer days due to strikes ( o.e.)Or

Manufacturing has a lower mean.

Public admin. more variable/greater spread (interpreting SD) than manufacturing (o.e.)2 B1

B1

1H Section BNoWorkingAnswerMarkNotes4 (a) 0.9 9/10 or 90%1 B1 (b)

0.9, 0.8, 0.1 (fractions or %)

0.08, 0.09, 0.813

B1 B1 B1 (2 correct B1)

(c) or 0.18 awrt 2 M1 A1 (d) The testdoesnotappear to bea good predictorof tooth decay.Plus

Any justifying statement

e.g.

Out of every 11that got tooth decay2 were predictedto get itOr

only 2 had a positive result(These could be presented in reverse order)

SC: A correct statement about tooth decay such as ��few with decay tested positive�� will be allowed B1

2 B1

B1 (dep)

1H Section BNoWorkingAnswerMarkNotes5 (a)

All points plotted correctly(Within 1/2 square)

1 B1 (b) Positivecorrelation.The ��

More waterthemore hay��.

2 B1 B1

(c) = 20

= 6.5Evidence adding and divide by 7

20, 6.5 Any order(1 correct will give M1)

2 M1

A1

(d)(i) (ii)

Point(20,6.5ortheir point)plotted correctlyLine

through mean pointwith thecorrect slope.2 B1ft B1

(e) Line on graph from 32for M1

8.0(7.9 – 8.1 acceptable for both marks) or read from graph2 M1 A1ft

(f) Amount from graph Intercept LOBF

Either

This is the

amount of hay produced due to rain only.OR

Extrapolation(extending beyond the line)not reliable.2 B1

B1

1H Section BNoWorkingAnswerMarkNotes6 (a) 96.5 (ISW)1 B1 (b) Must be pair for 2^{nd}B1

9393929191103113105.51021082 B1 B1

(c) IQR =

1.5 IQR + ?

Limit of outliers

102013.5111715+30+20.25+16.5+25.5+118143125.75118.5133.53 M1 M1

A1

(d) Box with whiskers

Median correct

Quartiles correct3 M1 A1 ft

A1 ft

(e) Box plot do not have to be drawn to get these marks Any 2 from EITHER

First bornhavehigher median. (not mean)OR

First bornhavegreater inter quartile range./range spread/variation (Don��t allow 2 of these)

OR

Both positive skew2 B1B1 (f) Collect more data1 B1

1H Section BNoWorkingAnswerMarkNotes7 (a) P(confirm) =or( 0.8) 80%(oe)1 B1 (b) P(not confirm) = 1 – P(confirm)or (0.2)20%(oe)1 B1ft (c)(i)

(ii)

P(3 confirm) = 4p^{3}q= 4 ��

p^{4}= = 0.410.41(awrt) or 256/625ISW

(M1 for working which give a second probability you may see

0.4096 0.1536 0.0256 0.0016– make sure the first is not from (i)For second

0.41

3 and 4 confirmations.5 M1 A1

M1

A1

A1

1H Section BNoWorkingAnswerMarkNotes8 (a) 31 B1 (b) Any ONE from: The weather is better.

Summer

It is the recognised holiday season

It is the main

school holidaytime.Prices higher

More people visit UK

1

B1 (c) 1 Attempt to add and divide

2700, 2700

(1 correct implies M1)

2

M1

A1

(d) Bothplotted correctly.1 B1 ft (e) Earnings (fairly) level or rise a little(until the end of 2000)

Earningsdecreased2 B1

B1

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