Key: 18 5 = 1.85 cm. 5 a Stem Leaf. Key: 2 0 = 20 points. b Stem Leaf Key: 2 0 = 20 cm. 6 a Stem Leaf. c Stem Leaf

Transcription

1 Answers EXERCISE. D D C B Numerical: a, b, c Categorical: c, d, e, f, g Discrete: c Continuous: a, b C 9 C Categorical B A Categorical and ordinal Discrete Ordinal D EXERCISE. Stem Leaf Key: = Stem Leaf Key: = $ The busker s earnings are inconsistent. Stem Leaf Key: =.% Stem Leaf Key: =. cm a Stem Leaf * * Key: = points b Stem Leaf Key: = cm a Stem Leaf Key: = cm b Stem Leaf * * Key: = cm c Stem Leaf Key: = cm a b 9 MATHS QUEST FURTHER MATHEMATICS VCE Units and

2 c d 9 e Stem Leaf Key: = years It seems to be an activity for older people. 9 C Stem Leaf * * * Key: = years More than half of the parents are or older with a considerable spread of ages, so this statement is not very accurate. Stem Leaf * 9 * 9 9 * Key: = hit outs Bulldogs, Melbourne, St Kilda Stem Leaf 9 Key: = $ The stem plot shows a fairly even spread of rental prices with no obvious outliers. a Stem Leaf Key: = mm b Stem Leaf * * Key: = mm c Stem Leaf Key: = mm Values are bunched together; they vary little. Stem Leaf 9 9 Key: = shots Stem Leaf * 9 * * Key: = net score The handicapper has done a good job as most of the net scores are around the same scores; that is, in the s. a Stem Leaf 9 b Stem Leaf * * Key: = % * * Key: = % Topic UNIVARIATE DATA

3 a b Computer lasts longer but is not as consistent. Computer is more consistent but doesn t last as long. a Year Stem Year Key: = cm b As you would expect the Year students are generally taller than the Year students; however, there is a large overlap in the heights. EXERCISE. y Number of students Number of students Computer Stem Computer 9 Key: = minutes x 9 Number of questions completed 9 Number of hours 9 Hours/week a b c 9 Height (cm) Class Class Class interval 9 Class interval Score MATHS QUEST FURTHER MATHEMATICS VCE Units and

4 Fish 9 Fatalities Ad Br Ca Co Es Fr Ge GWS Participation in activities 9 D Me years.% years.% years.% years % years.% and over.% GC Ha NM PA Ri St Syd WC The statement seems untrue as there are similar participation rates for all ages. However, the data don t indicate types of activities. times Score Log (weight (kg)) WB Check your histograms against those shown in the answer to question. D Check your histogram against that shown in the answer to question. 9 Number of students Number of families 9 9 Number of children a B b A c D A B 9 Number of hours spent on homework Number of days Tally 9 9 Number of days Topic UNIVARIATE DATA

5 a b a Attendance (s) 9 NZ.% US.% UK.% India.% China.% Thailand.% Fiji.% Singapore.% HK.9% Malaysia.% NZ.% US.% UK.% India.% China.% Thailand.% Fiji.% Singapore.% HK.9% Malaysia.% 9 Year b Check your bar chart against that shown in the answer to part a. EXERCISE. Positively skewed Negatively skewed a Symmetric b Negatively skewed c Positively skewed d Symmetric e Symmetric f Positively skewed a Symmetric, no outliers b Symmetric, no outliers c Symmetric, no outliers d Negatively skewed, no outliers e Negatively skewed, no outliers f Positively skewed, no outliers E C Negatively skewed Positively skewed. This tells us that most of the flight attendants in this group spend a similar number of nights (between and ) interstate per month. A few stay away more than this and a very few stay away a lot more. 9 a Symmetric b This tells us that there are few low-weight dogs and few heavy dogs but most dogs have a weight in the range of to 9 kg. a Symmetric b Most students receive about $ (give or take $). a Positively skewed b i ii % a Positively skewed b Since most of the data is linked to the lower stems, this suggests that some students do little exercise, but those students who exercise, do quite a bit each week. This could represent the students in teams or in training squads. a Club A: negatively skewed Club B: positively skewed b Since Club A has more members of its bowling team at the higher stems as compared to Club B; you could say Club A has the older team as compared to Club B. c i Club A: members over years of age ii Club B: members over years of age. a Cars sold b Positively skewed Apr May Jun Jul Aug Sep Oct Nov Month c June, July and November represent the months with the highest number of sales. d This is when the end of financial year sales occur. EXERCISE. Median = Median =. goals IQR = IQR = IQR =. IQR =. Median Range Mode a, 9 b c, d. e,, MATHS QUEST FURTHER MATHEMATICS VCE Units and

6 9 a b Median Range a b 9 c d e. f g 9 h. 9 i c The IQRs (middle %) are similar for the two restaurants, but they don t give any indication about the number of cars in each data set. An example is 9. There are many others. a The lowest score occurs several times. An example is. b There are several data points that have the median value. An example is. C Median Interquartile range Range Mode a,, b. 9 c..9. Median Interquartile range Range Mode a 9 b The data in set a have a greater spread than in set b, although the medians are similar. The spread of the middle % (IQR) of data for set a is bigger than for set b but the difference is not as great as the spread for all the data (range). a Range =, Median =., Mode =, IQR = b Range = Median = Mode = IQR = Median =, Mode = Q =., Q =., IQR =.9, Median =. a Median = 9, Q = 9., Q = 9, IQR =., Range =, Mode = 9 b The average handicap of the golfer s should be around. EXERCISE. Range = 9 Median = IQR = 9 Range = Median =. IQR =. They could represent the same data. They could represent the same data. a 9 9 Results out of Negatively skewed; % of results are between and. Fairly symmetrical Height jumped b The data is symmetrical and. is an outlier. Litres of fuel. is an outlier. Range Interquartile range Median a b c d e a iii b iv c i d ii The boxplots should show the following: Minimum value Q Median Q Maximum value a. b 9 c.... d. e D Topic UNIVARIATE DATA 9

7 9 Number of clients seen in a day See boxplot at foot of the page* a Median = Q = Q = 9 Min x =, Max x = IQR = is an outlier 9 Number of rides The data are negatively skewed with an outlier on the lower end. The reason for the outlier may be that the person wasn t at the show for long or possibly didn t like the rides. a Two similar properties: both sets of data have the same minimum value and similar IQR value. b Boys IQR = Girls IQR =. c The reason for an outlier in the boys data may be that the student did not understand how to do the test, or he stopped during the test rather than working continuously. Median =, Q = 9, Q =, Min x =, Max x = Weight (kg) Median = Q =. Q = Min x =, Max x = IQR =. is an outlier Number of times perform used per week 9 a Median = Q =. Q = Min x =, Max x = 9 IQR =. b No outliers c Check your boxplot against that shown in the answer to part a. EXERCISE..... a. b. c.9 d. e. a.. No, because of the outlier. b Yes c. Yes d. No, because of the outlier. D 9 A 9 a Median b Mean c Median d Median a.9 b. c. d. a. b Median = The distribution is positively skewed confirmed by the table and the boxplot.. papers Approximately fish. kg a Approximately cups b The median is., approximately cups. c The data is negatively skewed. EXERCISE.9. cents.% 9.9. a. b. * 9 9 Temperature ( C) MATHS QUEST FURTHER MATHEMATICS VCE Units and

8 c. d. e..%. m. seconds 9.9 C.9 km/h. pens.9 C x =., s =.. players. EXERCISE. Answers will vary. Answers will vary. B Answers will vary. Answers will vary. Population is larger, since a sample is taken from the population. C E 9 Yes, because the distribution is reasonably symmetric with no outliers B C Answers will vary. Answers will vary. Answers will vary. EXERCISE. a % of group s concentration span falls between secs and secs b 9% of group s concentration span falls between secs and secs c 99.% of group s concentration span falls between secs and 9 secs a % of the group to lie between. mm and. mm b 9% of the group to lie between. mm and. mm c 99.% of the group to lie between 9.9 mm and. mm a.% b % c % d.% a % b.% c % d 9.% bags a containers b containers c containers.. 9 a Specialist: μ =, σ = 9 English: μ =, σ = z s =., z e =. b English has the higher result as it has the higher z-score. a English., Maths. b Maths mark is better as it has a higher z-score. a Yes b Yes c No d No e No f Yes a and b and c and a. and. b. and. c. and.9 a. mm and. mm b. mm and. mm c. mm and. mm a and 9 b and c and C a.% b.% c % d.% e.% a i ii 9 iii b 9 a. b. c. B d. e. Second test, Barbara s z-score was. compared to. in the first test. a Barn: μ =. σ =. FR: μ=. σ =. b. c % d Cage Barn Free range Min x..9. Q. med... Q... Max x..9. i Cage:. Barn:. Free:. ii It could be concluded that the more space a chicken has, the fewer eggs it lays because the median is greatest for cage eggs. Topic UNIVARIATE DATA