statistics1历年考试真题分类汇编.docx

1、statistics1历年考试真题分类汇编Section A1Representation of data .Measures of location. Measures of spreadSection B9ProbabilitySection C14Permutations and combinationsSection D19Probability distributionsExpectation and Variance of a random VariableSection E22The binomial distributionSection F26The normal distr

2、ibutionAnswer30Section A30Section B36Section C39Section D40Section E42Section F44Section A Representation of data Measures of location Measures of spread1 The weights in kilograms of two groups of 17-year-old males from country P and country Q are displayed in the following back-to-back stem-and-lea

3、f diagram. In the third row of the diagram,. . . 4 | 7| 1 . . . denotes weights of 74 kg for a male in country P and 71kg for a male in country Q.(02w) (i) Find the median and quartile weights for country Q. 3(ii) You are given that the lower quartile, median and upper quartile for country P are 84,

4、 94 and 98 kg respectively. On a single diagram on graph paper, draw two box-and-whisker plots of the data. 4(iii) Make two comments on the weights of the two groups. 22 (i) (03s) The diagram represents the sales of Superclene toothpaste over the last few years. Give a reason why it is misleading. 1

5、(ii) The following data represent the daily ticket sales at a small theatre during three weeks.52, 73, 34, 85, 62, 79, 89, 50, 45, 83, 84, 91, 85, 84, 87, 44, 86, 41, 35, 73, 86.(a) Construct a stem-and-leaf diagram to illustrate the data. 3(b) Use your diagram to find the median of the data. 13 A r

6、andom sample of 97 people who own mobile phones was used to collect data on the amount of time they spent per day on their phones. The results are displayed in the table below. (03s)Time spent per day(t minutes)0 t 55 t 1010t 2020t 3030t 4040 t 70Numberof people 11 20 32 18 10 6(i) Calculate estimat

7、es of the mean and standard deviation of the time spent per day on these mobile phones. 5(ii) On graph paper, draw a fully labelled histogram to represent the data. 44 A computer can generate random numbers which are either 0 or 2. On a particular occasion, it generates a set of numbers which consis

8、ts of 23 zeros and 17 twos. Find the mean and variance of this set of 40 numbers. 4 (03w)5 The floor areas, x m2, of 20 factories are as follows. (03w)150 350 450 578 595 644 722 798 802 9041000 1330 1533 1561 1778 1960 2167 2330 2433 3231Represent these data by a histogram on graph paper, using int

9、ervals0 x 500, 500 x 1000, 1000 x 2000, 2000 x 3000, 3000 x 4000. 46 Two cricket teams kept records of the number of runs scored by their teams in 8 matches. The scores are shown in the following table. (04s)Team A150 220 77 30 298 118 160 57Team B166 142 170 93 111 130 148 86(i) Find the mean and s

10、tandard deviation of the scores for team A. 2The mean and standard deviation for team B are and respectively.(ii) State with a reason which team has the more consistent scores. 27 In a recent survey, 640 people were asked about the length of time each week that they spent watching television. The me

11、dian time was found to be 20 hours, and the lower and upper quartiles were 15 hours and 35 hours respectively. The least amount of time that anyone spent was 3 hours, and the greatestamount was 60 hours. (04s)(i) On graph paper, show these results using a fully labelled cumulative frequency graph. 3

12、(ii) Use your graph to estimate how many people watched more than 50 hours of television each week. 28 The lengths of cars travelling on a car ferry are noted. The data are summarised in the following table. (04w) Length of car (x metres)FrequencyFrequency density x 1785 x 24240 x 19190 x 8a9 The ag

13、es, x years, of 18 people attending an evening class are summarised by the following totals: x = 745, x2 = 33 951. (04w)(i) Calculate the mean and standard deviation of the ages of this group of people. 3(ii) One person leaves the group and the mean age of the remaining 17 people is exactly 41 years

14、. Find the age of the person who left and the standard deviation of the ages of the remaining 17 people. 410 The following table shows the results of a survey to find the average daily time, in minutes, that a group of schoolchildren spent in internet chatrooms. (05s)Time per day (t minutes)Frequenc

15、y0 t 10210 t 20f20 t 401140 t 804The mean time was calculated to be minutes.(i) Form an equation involving f and hence show that the total number of children in the survey was 26. 4(ii) Find the standard deviation of these times. 211 The following back-to-back stem-and-leaf diagram shows the cholest

16、erol count for a group of 45 people who exercise daily and for another group of 63 who do not exercise. The figures in brackets show the number of people corresponding to each set of leaves. (05s)(i) Give one useful feature of a stem-and-leaf diagram. 1(ii) Find the median and the quartiles of the c

17、holesterol count for the group who do not exercise. 3You are given that the lower quartile, median and upper quartile of the cholesterol count for the group who exercise are , and respectively.(iii) On a single diagram on graph paper, draw two box-and-whisker plots to illustrate the data. 412 A grou

18、p of 10 married couples and 3 single men found that the mean age of the 10 women was years and the standard deviation of the womens ages was years. For the 13 men, the mean age was years and the standard deviation was years. (05w)(i) Find the mean age of the whole group of 23 people. 2(ii) The indiv

19、idual womens ages are denoted by and the individual mens ages by . By firstfinding and , find the standard deviation for the whole group. 513 A study of the ages of car drivers in a certain country produced the results shown in the table. (05w)Percentage of drivers in each age groupYoung Middle-aged

20、ElderlyMales4035 25Females20 70 10Illustrate these results diagrammatically.14 The salaries, in thousands of dollars, of 11 people, chosen at random in a certain office, were found to be:40, 42, 45, 41, 352, 40, 50, 48, 51, 49, 47.Choose and calculate an appropriatemeasure of central tendency (mean,

21、 mode or median) to summarise these salaries. Explain briefly why the other measures are not suitable. 3 (06s)15 Each father in a random sample of fathers was asked how old he was when his first child was born. The following histogram represents the information. (06s) (i) What is the modal age group

22、 1(ii) How many fathers were between 25 and 30 years old when their first child was born 2(iii) How many fathers were in the sample 2(iv) Find the probability that a father, chosen at random from the group, was between 25 and 30 years old when his first child was born, given that he was older than 2

23、5 years. 216 32 teams enter for a knockout competition, in which each match results in one team winning and the other team losing. After each match the winning team goes on to the next round, and the losing team takes no further part in the competition. Thus 16 teams play in the second round, 8 team

24、s play in the third round, and so on, until 2 teams play in the final round. (06s)(i) How many teams play in only 1 match 1(ii) How many teams play in exactly 2 matches 1(iii) Draw up a frequency table for the numbers of matches which the teams play. 3(iv) Calculate the mean and variance of the numb

25、ers of matches which the teams play. 4 17 The weights of 30 children in a class, to the nearest kilogram, were as follows.50 45 61 53 55 47 52 49 46 5160 52 54 47 57 59 42 46 51 5356 48 50 51 44 52 49 58 55 45Construct a grouped frequency table for these data such that there are five equal class int

26、ervals with the first class having a lower boundary of 41.5 kg and the fifth class having an upper boundary of 61.5 kg. 4 (06w)18 In a survey, people were asked how long they took to travel to and from work, on average. The median time was 3 hours 36 minutes, the upper quartile was 4 hours 42 minute

27、s and the interquartile range was 3 hours 48 minutes. The longest time taken was 5 hours 12 minutes and the shortest time was 30 minutes. (i) Find the lower quartile. 2 (06w)(ii) Represent the information by a box-and-whisker plot, using a scale of 2 cm to represent 60 minutes. 419 The length of tim

28、e, t minutes, taken to do the crossword in a certain newspaper was observed on 12 occasions. The results are summarised below.(t 35) = 15 (t 35)2 = Calculate the mean and standard deviation of these times taken to do the crossword. 4 (07s)20 The lengths of time in minutes to swim a certain distance

29、by the members of a class of twelve 9-year-olds and by the members of a class of eight 16-year-olds are shown below. (07s)9-year-olds: 16-year-olds: (i) Draw a back-to-back stem-and-leaf diagram to represent the information above. 4(ii) A new pupil joined the 16-year-old class and swam the distance.

30、 The mean time for the class of nine pupils was now minutes. Find the new pupils time to swim the distance. 321 The stem-and-leaf diagram below represents data collected for the number of hits on an internet site on each day in March 2007. There is one missing value, denoted by x. (08s) (i) Find the median and lower quartile for the number of hits each day. 2(ii) The interquart