4. (i) As the age of the students increases, the length of time online increases


(ii) Based on this data, time spent online increases with age


(iii) Sample size is small, may not be random so may not be representative, don’t know how many of each age group were asked


(iv) Ask more students, make sure sample is representative, ask the same number of each age group


5. (i) Visitors increase from April to August and then decrease from August to November


(ii) People would be on Christmas holidays so might want to visit


(iii) The data suggests the centre may have been closed in February and March (no visitors)


6. (i) A tally and frequency table, a bar chart or pie chart to compare males to females


(ii) No: the data suggests this but more males (20) were questioned than females (10)


(iii) Mean number of bars eaten by males and females suggests males and females eat a similar amount of chocolate bars


7. (i)


Bicycle took less than 30 minutes every day: mean = 26, median = 25.5, mode = 25 and range = 6


(ii) Removing the extreme time (57 minutes), mean = 25, median =24 and mode = 21, all lower than bicycle averages


8. Most of the males weigh 50–60 kg (modal weight), this is the weight with the lowest frequency for females Females weights vary more and are more unevenly spread than males weights which lies mainly between 40–70 kg Females weights are mainly either very low or high


9. Disagree: the most popular time for ice creams is June–August (summer) so there is not enough evidence to suggest the advertisement worked


10.Disagree: many factors affect global warming there is no evidence to suggest a connection between pirates and global warming; the observation is coincidental


Practice questions 26.5


1. (i) 150 students, 25 from each year, randomly selected from the roll


(ii) Students chosen could all be from the same year; All students have equal chance of being picked


(iii) Sample size is very small; not all students have an equal chance of being picked


(iv) Not all students have an equal chance of being picked; only First Years chosen so sample is not representative


588 Linking Thinking 1


(v) Not all students have an equal chance of being picked; friends so may be biased


(vi) Sample may not be representative


2. Only 1 rollercoaster is above 50 metres, and most are a lot smaller; The mean is 50 metres due to the extreme value of 110 metres; The median of 38 metres would be a more accurate average


3. (i) Mean = €42 200; mode = €8 000; median = €8 000


(ii) No: only one employee earns more than the mean and most earn a lot less; the mean is affected by the one extreme wage of €175 000


(iii) The median, as it is not affected by extreme values


4. (i)


Girls participate more in all sports; a lot fewer boys participate in cross country than girls


(ii) The boys scale goes up in 5s, the girls in 2s; The width of the bars in the girls’ graph is bigger than in the boys’ graph; The gap between the bars on the girls’ graph is narrower than on the boys’ graph


(iii) Have both scales going up by the same amount, make the widths of the bars the same and make the gap between the bars the same


5. To produce the desired response to the data; Starting the scales at different points, altering the width of the bars or the gap between the bars, use of 3D effects, shading, colour, etc.


Revision questions


26A Core skills 1. (a)


(i) Mode = red (ii) Mode = dog


(b) Data is categorical


2. (i) Median = 34, mean = 36·25 (ii) Median = 15, mean = 16·46


3. (i) Mean = 22, median = 19·5, mode = 12, range = 26


(ii) Mean = 21·9, median = 22, mode = 5, range = 43


(iii) Mean = 48·64, median = 52, mode = 72, range = 66


(iv) Mean = 42·11, median = 40, mode = 51, range = 51


4. Mean = 69·36, median = 70·5, mode = 84, range = 66


5. (i) 96 kg, (ii) 115 kg 6. (i) 14·8°C, (ii) 1·7°C 7. (i) Line plot, because it is easy to draw and the data set is small


(ii) 4 children (iii) 3·4 (iv) 3·5 (v) 4 is a whole and you can’t have fractions of children


26B Taking it further


1. (i) €46, (ii) €40, (iii) €70 2. (ii) 34 litres (iii) 31 litres (iv) 30 litres


4. (i) Alpha United, they won 3 matches


(ii) No, Alpha United won 3


OR Yes, Alpha United only won 9 matches and Beta Rovers won 19 matches


__ 3;


5. (i) This scale starts at 25 instead of 0 (ii) To make his sales look bigger (iii) Pie chart (iv) The mode is the highest average so this would be best to show the highest sales: mean = 37.5, median = 36.5 and mode = 44


Unit 27 Probability 2


Practice questions 27.1 1. (i) 1


2. (i) 20 (ii) Numbers should appear as (a)


_ 6, (ii) 5


_ 6, (iii) 1


_ 2, (iv) 0


P(Green) = 1


3. (i) 36 (ii) 1


(iii) Star; any valid justification, e.g. there are more stars than any other shape


_ 6


(iv) Star, as its probability = 9


4. (i) Coffee + muffin; tea + muffin; juice + muffin; coffee + cookie; tea + cookie; juice + cookie; coffee + fruit pot; tea + fruit pot; juice + fruit pot


(ii) 1 (iii) 1


__ 9


5. 0·1 6. (i) P(lose) = 0.6 7. Possible outcomes = (Y, Y), (Y, R), (R, R), (R, Y)


_ 3


Practice questions 27.2


1. 0·1 2. 0·24 3. (i)


0·7


(ii) Any mathematical justification, e.g. the general belief is incorrect, or more trials needed


4. (i) 8 (ii) 252


5. (i) A = 600, B = 0·125, C = 0·2, D = 0·15, E = 0·3, F = 1


6. (i) G = 4, 0.2; R = 7, 0.35; Y = 5, 0.25 (ii) The second table provides the best estimate, as sample size is much larger


(ii) Collie (iii) 750


7. (i) Frequency: 4, 3, 3, 2, 3, 5 Relative frequency: 0.2, 0.15, 0.15, 0.1, 0.15, 0.25


(ii) 15 times (iii) Expected 6 in fair die = 10, number of 6 with this die = 15


(iv) Die may be biased, more trials needed to confirm


__ 36 = 25%


P(not red) = 11


__ 4 ; (b) P(Blue) = 3


__ 20


__ 10; (c)


3. (i) Disagree, the mean is 5 (ii) She may have just counted the numbers and called that the mean


__ 4 of their


matches but Beta Rovers only won 1


__ 4 of their


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