Grade 11 - STMG / statistics 29 exercises (100% corrected)

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12345678910ABCDEFG75-5312-211212584233-6-5435-5139 123456789101112131415161718ABCDEAnnéesdesjeuxdupaci∏queNombredemédaillesd’orNombredemédaillesd’argentNombredemédaillesdebronzeTotal16937911271966393030991969362021771971333227921975373134102197933432610219832420196319878248381681991292927851995825743182199973554417220039373742032007906968227Total:6585164621636Moyennes:514036126 1234567ABCDEFGHIJKLMNNote012345678945E∑ectifs0034143514250061242018358361390Note1011121314151617181920145E∑ectifs5423002110018504424390032171800224 1234567891011121314ABCDEFGHIJL.M.Mer.J.V.S.D.TotalMoyenneSemaine11571451421591901561611110159Semaine21471581561411411521551050150Semaine31531481621491601461631081154Semaine41681561621571661581611128161Semaine51631691701621671691621162166Semaine61561671711731651651621159166Semaine71731721681731611621671176168Semaine81681661701731681761651186169Semaine91761751751711721781731220174Semaine101891761721801851711711240177Semaine111781811831721781721731237177Semaine121711831711841721761731230176Moyennesurtroismois166 1. Reminders: calculation sheets E.7297 1 Check the boxes E7 et B10 . 2 Given that an empty box has a value of zero, calculate the value of the following two formulas : a A : =B3+C1+F2+E5 b B : =A7+D10+D9+F4-C5 3 A range of cells is a set of cells expressed in the form ˇ C3:E5 ı designating all the cells contained in the rectan-gle with opposite corners at cells C3 et E5 . Surround this range of cells. 4 The functions SUM(...) et AVERAGE(...) calculate the sum and average of the values of the cells passed as ar-guments, respectively. Give the value of the following formulas : a SUM(C3:E5) b SUM(C1: C10) c MOYENNE(A3:F4) d SOMME(C1:C9)+SOMME(C5:G5) E.7254 The number of medals won by New Caledonian athletes at the Pacific Games was recorded. Here are the results grouped together in a table : 1 To obtain the number 27 in the cell E2 , we wrote the fol-lowing formula : SUM(B2:D2) . What formula has been written in B16 to obtain 658? 2 What formula has been written in B18 to calculate the average gold medals obtained over these 13 years? E.7352 Below is a spreadsheet representing the grades obtained by students in a class : The following operations have been integrated into the spread-sheet : the formula ˇ =SOMME(B1: K1) ı was entered in cell N1 , then copied down to the range N1:N7 ; the formula ˇ =B1*B2 ı was entered in cell B3 , then copied back to the left on range B3:K3 ; the formula ˇ =SOMME(B5*B6) ı was entered in cell B7 , then copied down to the range B7*L7 ; From this statistical series : a son total number b sa moyenne Results will be rounded to the hundredth if necessary. E.7255 From 2 January 2012 , an airline is testing a new flight between Nantes and Toulouse. The flight takes place every day aboard an aircraft that can carry a maximum of 190 passengers. Starting in February, we decide to study the frequentation of this bowl for twelve weeks. The company uses a spreadsheet showing the number of passengers per day. This spreadsheet is given below : 1 What formula has been entered in the cell I2 to obtain the total number of passengers during the week 1 ? 2 What formula has been entered in cell J2 to obtain the average number of passengers per day over the week 1 ? https://chingmath.fr chapExoCorrec/7297 sacados/7297 12345678910ABCDEFG75-5312-211212584233-6-5435-5139 chapExoCorrec/7254 sacados/7254 123456789101112131415161718ABCDEAnnéesdesjeuxdupaci∏queNombredemédaillesd’orNombredemédaillesd’argentNombredemédaillesdebronzeTotal16937911271966393030991969362021771971333227921975373134102197933432610219832420196319878248381681991292927851995825743182199973554417220039373742032007906968227Total:6585164621636Moyennes:514036126 chapExoCorrec/7352 sacados/7352 1234567ABCDEFGHIJKLMNNote012345678945E∑ectifs0034143514250061242018358361390Note1011121314151617181920145E∑ectifs5423002110018504424390032171800224 chapExoCorrec/7255 sacados/7255 1234567891011121314ABCDEFGHIJL.M.Mer.J.V.S.D.TotalMoyenneSemaine11571451421591901561611110159Semaine21471581561411411521551050150Semaine31531481621491601461631081154Semaine41681561621571661581611128161Semaine51631691701621671691621162166Semaine61561671711731651651621159166Semaine71731721681731611621671176168Semaine81681661701731681761651186169Semaine91761751751711721781731220174Semaine101891761721801851711711240177Semaine111781811831721781721731237177Semaine121711831711841721761731230176Moyennesurtroismois166
GarçonsFilles20406080100En tramwayEn véloA pieds 2028364452600510152025303540 2. Reminders: numbers and frequencies E.7351 After conducting a study on the means of transportation used by students to get to school, we obtained the diagram shown below : 1 Complete the double-entry table below : En Tram Bicycle Walking Total Girls Boys Total 2 The results will be rounded to 10 − 4 : a How often do girls use the tram to get to high school? b Among boys, how often do they come by bike? E.7259 In a company, the age of 125 employees was studied. The results of this study are shown in the following table : Age [20; 28[ [28; 36[ [36; 44[ [44; 52[ [52; 60[ Total Number of employees n i 15 35 40 10 Frequencies in % 1 Complete the table above. 2 Draw a histogram of the workforce using the grid below. 3 a How many employees are under 44 years old? b How many employees are 36 years old or older? c What percentage of employees are between 52 and 60 years old? 3. Reminders: cumulative frequencies E.7257 A survey looks at the number of books read by ninth-grade students at a school. Here are the survey results shown in the table below : Number of books 0 1 2 3 [4;8[ [8;12[ [12;20[ Number of students 3 5 20 12 5 2 2 Number of students cumulative ascending Number of students cumulative descending 1 Complete this table. 2 Answer the following questions : a How many students read at least 8 books? b How many students read at most 11 books? https://chingmath.fr chapExoCorrec/7351 sacados/7351 GarçonsFilles20406080100En tramwayEn véloA pieds chapExoCorrec/7259 sacados/7259 2028364452600510152025303540 chapExoCorrec/7257 sacados/7257
E.7298 In a study group, the height of each stu-dent was recorded. This allowed us to obtain the following statistical series : 1 m 62 ; 1 m 55 ; 1 m 58 ; 1 m 51 ; 1 m 60 ; 1 m 73 ; 1 m 69 ; 1 m 65 1 m 62 ; 1 m 54 ; 1 m 66 ; 1 m 56 ; 1 m 59 ; 1 m 60 ; 1 m 64 ; 1 m 57 1 m 72 ; 1 m 58 ; 1 m 67 ; 1 m 52 ; 1 m 70 ; 1 m 62 ; 1 m 51 ; 1 m 74 1 Give the total number of students in this group. 2 Calculate the average height of this group, rounded to the nearest centimeter. 3 We are constructing classes with an amplitude of five centimeters. Complete the following table : Classes [1.50;1.55[ [1.55;1.60[ [1.60;1.65[ [1.65;1.70[ [1.70;1.75[ Number of students Effectif cumulative ascending Effectif cumulative descending Frequency (en %) Frequency cumulative descending (en %) Note: frequencies will be rounded to the nearest hun-dredth. 4 a How many people are 1 m 65 or shorter? b How many people are taller than 1 m 65 ? c How many people are 1 m 60 or taller? 4. Average and statistical series E.7232 We asked 10 people how many times they had visited a museum in the last month. Here are their answers : 2 ; 0 ; 4 ; 1 ; 0 ; 2 ; 3 ; 2 ; 1 ; 2 1 Give the percentage frequency of ˇ people who visited a museum twice in the last month ı. 2 Determine the average number of visits this group made to a museum in the last month. E.7256 Ms. A and Mr. B are both math teachers and both have a ninth-grade class with 20 students. They compare the grades their students received on the last common assignment : Grades given by Grades given by Ms. A Mr. B 7 - 8 - 12 - 12 - 18 - 5 - 11 8 - 8 - 9 - 12 - 11 - 8 - 13 18 - 9 - 20 - 6 - 16 - 6 - 18 10 - 12 - 8 - 10 - 14 - 12 - 11 7 - 15 - 6 - 3 - 8 - 5 14 - 9 - 15 - 7 - 9 - 10 Calculate the average for each series. 5. Average and staffing table E.7231 To market tomatoes, a cooperative grades them according to their diameter. Below is a list of the diameters of 30 tomatoes (in millimeters) . 49 - 52 - 59 - 57 - 51 - 55 - 50 - 56 49 - 48 - 58 - 49 - 52 - 51 - 53 - 56 49 - 56 - 55 - 50 - 52 - 56 - 57 - 54 53 - 49 - 51 - 55 - 56 - 59 1 Reproduce and complete the following table : Diameters [48 ; 51[ [51 ; 54[ [54 ; 57[ [57 ; 60[ Number 8 Class center 52.5 2 a Using this table of numbers, verify that the average diameter of a tomato is 54 mm , rounded to the nearest whole number. b Determine the volume, in mm 3 , of a tomato of aver-age diameter, modeled as a sphere. Take ı ≈ 3.1416 and round to the nearest whole number. Reminder : the volume of a sphere with radius R is 4 3 × ı × R 3 https://chingmath.fr chapExoCorrec/7298 sacados/7298 chapExoCorrec/7232 sacados/7232 chapExoCorrec/7256 sacados/7256 chapExoCorrec/7231 sacados/7231
N N N N E.7258 In a survey of 671 students at a middle school, the amount of time d (in minutes) spent by each doing their schoolwork each day is recorded. The results have been grouped into four classes in the table below : 1 Complete this table, rounding frequencies to 1% . Durées de travail (en minutes) 0 d< 30 30 d< 60 60 d< 90 90 d< 120 Total Effectifs 106 235 144 671 Fréquences en pourcentage 16 100 2 Replacing each class with its center, calculate the aver-age time a student spends each day doing schoolwork, rounded to the nearest minute. 6. Structure effect E.7283 In the company A , the salary of an ex-ecutive is 2 800 euros and that of a non-executive employee is 2 100 euros. In company B , the salary of an executive is 3 100 euros and that of a non-executive employee is 2 300 euros. 1 Conjecture which company has the highest average salary? 2 In the table below, are represented the number of employ-ees in each socio-professional category in each company: Company A Company B Cadres 237 63 Non-executives 112 188 Total a Complete the table. b Determine the average wage, rounded to the nearest cent, for each of the companies. 7. Reminders: median and quartiles E.7196 1 Here are the marks of four groups of students in the brevet blanc. Complete the boxes for the various indica-tors below : Group 1 Group 2 Group 3 Group 4 Scores 5 - 6 - 10 10 - 11 12 - 12 14 6 - 8 - 8 8 - 10 - 11 14 - 15 8 - 8.5 8.5 - 9 11 - 11 12 - 12 6 - 6 - 7 8 - 10 - 11 11 - 15 Average Range Median 2 Comparer from a qualitative point of view in the light of the indicators calculated above : a Group 1 and Group 2 b Group 2 and Group 4 c Group 1 and Group 3 E.7197 On a graduated line, a teacher has or-dered the grades of these four classes of 10th graders. Here are their representations : Series 1: Series 2: Series 3: Series 4: 1 Show the median value Me of the series on each of the graduated lines. 2 Plot on each of the graduated lines the value of the first quartile Q 1 and the third quartile Q 3 . 8. Quartiles and increasing cumulative frequency curves E.7228 Here is the table showing the students’ grades in the middle school diploma exam: Grade 0 ; 4 4 ; 8 8 ; 12 12 ; 16 16 ; 20 Number of students 5 32 61 80 15 Freq. Cumulative freq. Ascending https://chingmath.fr chapExoCorrec/7258 sacados/7258 chapExoCorrec/7283 sacados/7283 chapExoCorrec/7196 sacados/7196 chapExoCorrec/7197 sacados/7197 N N N N chapExoCorrec/7228 sacados/7228
0123456789 10111213141516171819200.10.20.30.40.50.60.70.80.91 02030405060700.20.40.60.81 1 What is the modal class in this statistical series? 2 Calculate the school average for this exam, rounded to the nearest tenth. 3 a Complete the table by rounding the frequencies to the nearest thousandth. b In the graph below, plot the curve of the cumulative frequencies. c Deduce the value of the median. (Leave the construc-tion lines visible) E.7281 The senior classes at a school take the sports test in javelin throwing. When reviewing the test, the results of the four senior classes were compiled in the table below : Longueur (in m ) 20 ; 30 30 ; 40 40 ; 50 50 ; 60 60 ; 70 Number of students 5 34 30 18 5 Frequency Cumulative frequency Increasing 1 Complete the table with the frequencies and cumulative frequencies, rounding the results to two decimal places. 2 In the graph below, draw the polygon of cumulative fre-quencies : 3 Graphically, determine the value of the median and quar-tiles. (Leave the construction lines in place.) . https://chingmath.fr 0123456789 10111213141516171819200.10.20.30.40.50.60.70.80.91 chapExoCorrec/7281 sacados/7281 02030405060700.20.40.60.81
0102030400.10.20.30.40.5Duréedutrajet(enmin)Fréquence(en%) 0102030400.10.20.30.40.50.60.70.80.91Duréedutrajet(enmin)Fréquence(en%) 0246810121416182022242628303234363840 03040506070800.10.20.30.40.50.60.70.80.91 3035404550556065707580 E.7299 By studying the time it takes to travel to school for one class. Here are all the times : 5 ; 15 ; 15 ; 25 ; 5 ; 38 ; 37 ; 20 ; 3 ; 15 ; 7 ; 2 ; 30 ; 10 16 ; 2 ; 5 ; 5 ; 20 ; 25 ; 25 ; 30 ; 3 ; 11 ; 25 ; 8 ; 13 1 Complete the table below by rounding the frequencies to the nearest thousandth. Class (in min) 0 ; 10 10 ; 20 20 ; 30 30 ; 40 Number of students Frequency Fréquence Cumulé Croissant 2 Construct the frequency histogram below : 3 a Construct the cumulative frequency curve : b Using the cumulative frequency curve, determine the quartiles and median of this statistical series. c Construct the box plot associated with this statistical series : E.7353 After a meeting on the construction of line 5 of the Montpellier tramway, participants were asked about their âage. Here are the statistics obtained : 39 - 52 - 79 - 47 - 31 - 55 - 40 - 36 39 - 58 - 58 - 39 - 72 - 61 - 63 - 56 39 - 66 - 55 - 40 - 52 - 66 - 77 - 54 53 - 69 - 51 - 35 - 46 - 39 1 Reproduce and complete the following table. Round to the nearest thousandth if necessary : Age [30 ; 40[ [40 ; 50[ [50 ; 60[ [60 ; 70[ [70 ; 80[ Number of people Frequency Cumulative frequency increasing 2 Using a calculator, determine the mean and standard de-viation of the table of numbers. 3 a Plot the cumulative frequency curve in the graph below : b Deduce the first quartile, median, and third quartile of this statistical series, rounded to two decimal places. c Draw the associated box plot : 9. Quartiles and calculators E.7282 BMI stands for body mass index. In a study of 400 women, here is the BMI table for this popula-tion : IMC 19 20 21 22 23 24 25 26 27 28 29 Numbers 25 37 106 92 38 39 16 12 15 13 7 1 Using a calculator, determine the first quartile, median and third quartile of this statistical series. 2 Draw the box plot on the graduated line below : https://chingmath.fr chapExoCorrec/7299 sacados/7299 0102030400.10.20.30.40.5Duréedutrajet(enmin)Fréquence(en%) 0102030400.10.20.30.40.50.60.70.80.91Duréedutrajet(enmin)Fréquence(en%) 0246810121416182022242628303234363840 chapExoCorrec/7353 sacados/7353 03040506070800.10.20.30.40.50.60.70.80.91 3035404550556065707580 chapExoCorrec/7282 sacados/7282
181920212223242526272829303132 1010.51111.51212.5131881à19001901à19201921à19401941à19601961à1980 10. Comparing box plots E.7280 The Paris Montsouris weather station has been continuously recording outdoor temperatures since 1872 and provides annual averages based on these read-ings. The purpose of this exercise is to compare these averages for twenty-year periods between 1880 and 2000. To clarify the terminology, we will refer to the average of the temperatures recorded during a given year (days and nights), expressed in degrees Celsius and rounded to 0.05 o C . Sources Météo France The document below presents box plots constructed from an-nual temperatures during each twenty-year period between 1881 and 1980. Each of these plots shows the median, first quartile, and third quartile. The ends of the ˇwhiskersı mark the minimum and maximum values in this series. For each of the following statements, indicate whether it is true, false, or undecidable (if the document does not allow you to determine whether the statement is true or false) . Jus-tify your answer. 1 The maximum annual temperature was 12.65 o C for a century, from 1881 to 1980. 2 The range of annual temperatures was 2.25 o C for a cen-tury, from 1881 to 1980 3 For a century, from 1881 to 1980, at least thirty years had annual temperatures below 11.5 o C . 4 The year 1961 was the coldest in the period 1901-1980. 11. Standard deviations of a statistical series E.7301 The height (expressed in centimeters) of the students in a first-year class is being studied. Here are the data collected during the study : 167 − 181 − 173 − 179 − 165 − 169 − 170 − 174 − 160 172 − 173 − 164 − 170 − 156 − 161 − 171 − 174 − 162 183 − 176 − 170 − 163 − 175 − 155 − 173 − 167 − 168 175 − 170 − 162 − 169 − 170 − 159 Using a calculator, determine the mean and standard devia-tion of this statistical series. Results should be rounded to the nearest tenth. 12. Standard deviation of a staffing table E.7229 The table showing the grades of a class is given below : Grade 0;4 4;8 8;12 12;16 16;20 Number of students 2 5 10 7 3 Using a calculator, determine the mean and standard devia-tion of this statistical series. Give your results rounded to two decimal places. E.7277 A farmer grows tomatoes and must grade them before delivering them to supermarkets. Here are the tomatoes harvested according to their size : Diameter of the tomato 25 ; 35 35 ; 45 45 ; 55 55 ; 65 65 ; 75 Number of tomatoes 125 254 741 294 183 Using the calculator, determine the mean and standard devi-ation of this statistical series. https://chingmath.fr 181920212223242526272829303132 chapExoCorrec/7280 sacados/7280 1010.51111.51212.5131881à19001901à19201921à19401941à19601961à1980 chapExoCorrec/7301 sacados/7301 chapExoCorrec/7229 sacados/7229 chapExoCorrec/7277 sacados/7277
Rounding the values to two decimal places. E.7300 BMI stands for body mass index. In a study of 400 women, here is the BMI table for this popula-tion : IMC 19 20 21 22 23 24 25 26 27 28 29 Numbers 25 37 106 92 38 39 16 12 15 13 7 Using a calculator, determine the mean and standard devia-tion of this statistical series. Results should be rounded to the nearest hundredth. E.7230 The results will be rounded to two dec-imal places. Here are the 25 grades of ninth-grade students on a test : 10.5 - 4.5 - 9.25 - 11 - 8.5 - 8.5 - 15.5 - 5 13.5 - 7.5 - 6.5 - 12.5 - 15 - 13.25 - 17.25 - 5.75 2 - 13.25 - 15.5 - 6.5 - 7.25 - 12.75 - 7.25 - 15 - 8.75 1 Using a calculator, determine the mean and standard de-viation of the series. 2 a Complete the table below : Score 0 ; 2 2 ; 4 4 ; 6 6 ; 8 8 ; 10 Number of students Score 10 ; 12 12 ; 14 14 ; 16 16 ; 18 18 ; 20 Number of students b Using the table of numbers and your calculator, deter-mine the mean and standard deviation. 13. Standard deviation and centered interval E.7278 A call center has 24 call center agents. The HR department (Human Resources Department) has listed the number of calls made by its call center agents last week in the table below : Nombre calls 100 ; 120 120 ; 140 140 ; 160 160 ; 200 Number of call center agents 3 7 10 4 The values will be rounded to two decimal places. 1 Using a calculator, determine the mean and standard de-viation of this statistical series. 2 Give the expression for the interval x − 2 ff ; x +2 ff . E.7279 To verify the information marked on the packaging, a consumer organization removes 100 chocolate bars from a factory’s production line to check the chocolate content. The results of its study are shown in the table below : Cocoa content 80 81 82 83 84 85 86 87 88 89 90 Number of bars 1 2 5 12 16 19 15 14 10 4 2 The values requested will be rounded to two decimal places. 1 Using a calculator, determine the mean and standard de-viation of this statistical series. 2 a Express the interval x − 2 · ff ; x − 2 · ff . b What percentage of bars belong to the interval x − 2 · ff ; x +2 · ff ? E.7354 Jean, who is passionate about a video game, recorded the duration in seconds of the 40 games he played : 49 55 57 57 57 58 58 59 60 60 60 62 63 63 63 63 64 64 64 64 65 65 66 67 69 69 70 70 72 74 74 75 75 76 77 78 79 80 80 80 Note: the results will be rounded to the nearest thou-sandth. 1 Using a calculator, determine the mean and standard de-viation of this statistical series. 2 What is the frequency, expressed as a percentage, of games with a duration falling within the interval x − ff ; x + ff ? https://chingmath.fr chapExoCorrec/7300 sacados/7300 chapExoCorrec/7230 sacados/7230 chapExoCorrec/7278 sacados/7278 chapExoCorrec/7279 sacados/7279 chapExoCorrec/7354 sacados/7354