Grade 10 / Position and dispersion indicator 61 exercises (including 60 corrected)

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ChingQuizz : 6 exercises available for Quizz assessment : 1. Averages E.1912 Paul, Marie and Laurent get together to buy and put into a common fund 558 e in order to buy the PlagaStation3. Here’s a table of the sums donated by each of these people : Paul Marie Laurent 172 135 251 1 What is the percentage of the sum paid for each person, relative to the total price of the games console? (round to the nearest tenth of a degree.) 2 How much would each person have contributed, if the purchase had been fairly divided? E.214 1 Give the mean of the following statistical series rounded to the nearest hundredth : 8 ; 9 ; 12 ; 13 ; 10 ; 5.5 ; 7 2 We will give the requested values rounded to the nearest hundredth : a Give the mean of this series if we subtract 2 from each of the values in the series. b Give the mean of this series if we multiply each of the values in the series by 2. 2. Average and middle of the class E.1914 Here are the 25 grades of ninth graders 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 Calculate the average of these scores. 2 We decide to classify this statistical series into range 2 classes. Complete the following table : Note 0 ; 2 2 ; 4 4 ; 6 6 ; 8 8 ; 10 Headcount Note 10 ; 12 12 ; 14 14 ; 16 16 ; 18 18 ; 20 Headcount 3. Weighted average E.4754 Definition: Consider a statistical series whose individuals take the val-ues x 1 , x 2 , . . . , x k associated with n 1 , n 2 , . . . , n k , respec-tively. The average x of this series has the value : x = n 1 × x 1 + n 2 × x 2 + · · · + n k × x k n 1 + n 2 + · · · + n k Note that the sum n 1 + n 2 + ··· + n k is the total number of the statistical series. In a P.M.E. (small and medium-sized enterprise) , the person-nel manager summarizes the company’s various salaries in the following table : Fonction Ouvrier Cadre Dirigeant Salaire 1 253 2 612 3 841 Effectif 34 8 2 Values are rounded to the nearest euro. 1 Determine the average salary in this company. 2 The human resources directrion plans for the following year to : an increase of 12 % in the number of workers (rounded off to the nearest whole number) ; a reduction of 25 % in the number of managers ; and the retirement of one of the executives. With these details, estimate the average cost of a salary in this company the following year. https://chingmath.fr chapExoCorrec/1912 sacados/1912 chapExoCorrec/214 sacados/214 chapExoCorrec/1914 sacados/1914 chapExoCorrec/4754 sacados/4754
E.216 Here are the yearly averages and bac-calaureate coefficients for each of them. FR. Ph Ma LV1 LV3 HGE ESC EPS ECO SPE Alain 11 12 5 12 9 12 1 7 × 8 Bac L 5 7 2 4 4 4 2 2 × 4 FR. Ph Ma LV1 LV3 HGE ESC EPS ECO SPE Anne 12 5 9 12 11 5 5 13 15 9 Bac ES 4 4 5 3 3 5 2 2 7 2 FR. Ph Ma LV1 HGE SVT PHY EPS SPE Henry 5 2 15 8 10 9 12 11 15 Bac S 4 3 7 3 3 6 6 2 2 1 With the same baccalaureate grades as his yearly aver-ages, will Henry pass the bac? 2 a Justify that Alain will not get the baccalauréat with his annual averages and that he will go through the rattrapage. b Choosing mathematics as his remedial subject, what minimum mark must he have to pass the baccalauréat? E.217 Here are the 25 notes of ninth graders 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 Calculate the average of these scores. 2 We now decide to study this statistical series via the cor-responding headcount table : a Complete the staffing table below : Note 0 ; 2 2 ; 4 4 ; 6 6 ; 8 8 ; 10 10 ; 12 Number Note 12 ; 14 14 ; 16 16 ; 18 18 ; 20 Number b Determine the mean of this series, but calculated from the headcount table. E.210 In a high school are distributed as follows : 7 Seconde classes with an average of 32 students per class. 5 première classes with an average of 28 students per class. 4 classes of Terminales with an average of 25 students per class. 1 Determine the number of students in each level. 2 How many classes does this school have in total? 3 Deduct the average number of pupils per class for this establishment. 4. Averages and frequencies E.1995 Definition: Consider a statistical series whose individuals take the val-ues x 1 , x 2 , . . . , x k associated respectively with frequencies f 1 , f 2 , . . . , f k . The mean x of this series is : x = f 1 × x 1 + f 2 × x 2 + · · · + f k × x k Here are The results of the demographic census of the French population organized in 2007 . Classe d’âge [0 ; 20[ [20 ; 65[ [65 ;100] Effectif total Population 24.9 % 58.8 % 16.3 % 63 753 140 (for this exercise, the population aged over 100 is assumed to be negligible) 1 Determine the number of individuals in the French pop-ulation under the age of 20. 2 Determine the average age of the French population to the nearest year. 5. Average of average E.4752 The table below shows the maximum temperatures in a city over the course of a week: Monday Tuesday Mercr. Jeudi Vendr. Samedi Dim. 26.2 27 27.4 24.7 25.5 26 26.5 Results will be rounded to the nearest hundredth of a degree Celsius. 1 Determine the average maximum temperature during this week. 2 Knowing that over the previous two weeks the average of these maximum temperatures was 25.64 , determine the average maximum temperatures over these three weeks. https://chingmath.fr chapExoCorrec/216 sacados/216 chapExoCorrec/217 sacados/217 chapExoCorrec/210 sacados/210 chapExoCorrec/1995 sacados/1995 chapExoCorrec/4752 sacados/4752
E.1915 We have a statistical series that we di-vide into two subgroups. 1 The first subgroup has a mean of 12, and we know that the sum of the values in the series is 288. Determine the size of this subgroup. 2 The second group has a mean of 11.5 and its membership is 20. Calculate the mean of the entire series. E.225 In a high school, we are studying the size of three groups of students taking part in A.S. Here is a table summarizing their sizes : Group A 1.50 ; 1.60 1.60 ; 1.70 1.70 ; 1.80 2 5 3 Group B 1.50 ; 1.60 1.60 ; 1.70 1.70 ; 1.80 0 5 6 Group C 1.50 ; 1.60 1.60 ; 1.70 1.70 ; 1.80 3 4 1 The various calculations will be rounded to the nearest hun-dredth. 1 Calculate the average size of each study group. 2 No longer considering the three groups, but the 29 stu-dents participating in the AS, determine the average of the participants. 3 The following results are accepted : Groupe A Groupe B Groupe C Total headcount 10 11 8 Average group size 1.66 1.70 1.63 a Determine the average size of the three groups using the table above. b What do we notice? E.209 A statistical series is divided into two subgroups. 1 The first subgroup has a mean of 12 and the sum of the values in the series is 288. Determine the size of the first subgroup. 2 The second group has a mean of 11.5 and a membership of 20. Calculate the mean of the complete series to the nearest hundredth. E.4753 At the end of the month, a mechanic takes stock of his activities during the month. The table be-low summarizes his billings by amount : Prix [100 ; 200[ [200 ; 500[ [500 ; 1000[ [1000 ; 3000[ Effectif 32 51 17 3 Results will be rounded to the nearest euro. 1 Determine the average price of a repair in this month. 2 Knowing that in the previous month, this garage carried out 94 repairs with an average price of 365.12 e . Deter-mine the average price of a garage repair over the last two months. 6. Problems around the average E.208 A statistical series has a mean of 21, while the sum of its list of values is 273. How many numbers does this statistical series consist of? E.227 1 In a class of 31 students, the average age of the students is 15.5 years. Taking into account the age of the mathe-matics teacher, the class average rises to 15.86 years. Determine the professor’s age, rounding to the nearest year. 2 In a class of 33 students, the average annual math grade for 18 girls is 12.4 , and for boys is 11.2 . What is the average math grade for the class? We’ll round this average to the nearest hundredth. E.218 1 In mid-term, a student has 11 average. On the next test, the student gets a mark of 13 and his average rises to 11.5 . How many marks did he get then? 2 Before the end of the term, this student has an average of 12.75 with 5 grades. What mark does he need to achieve, on the last mark of the term, in order to have an average of 13 ? https://chingmath.fr chapExoCorrec/1915 sacados/1915 chapExoCorrec/225 sacados/225 chapExoCorrec/209 sacados/209 chapExoCorrec/4753 sacados/4753 chapExoCorrec/208 sacados/208 chapExoCorrec/227 sacados/227 chapExoCorrec/218 sacados/218
1481318815209592555930221355745315521070Age (ans)40 individus E.5070 The table below shows the maximum temperatures in a city over the course of a week: Monday Tuesday Mercr. Jeudi Vendr. Samedi Dim. 26.2 27 27.4 24.7 25.5 26 26.5 Results will be rounded to the nearest hundredth of a degree Celsius. 1 Determine the average maximum temperature during this week. 2 Knowing that over the previous two weeks the average of these maximum temperatures was 25.64 , determine the average maximum temperatures over these three weeks. E.5071 At the end of the month, a mechanic takes stock of his activities during the month. The table be-low summarizes his billings by amount : Prix [100 ; 200[ [200 ; 500[ [500 ; 1000[ [1000 ; 3000[ Effectif 32 51 17 3 Results will be rounded to the nearest euro. 1 Determine the average price of a repair in this month. 2 Knowing that in the previous month, this garage per-formed 94 repairs with an average price of 365 e . Deter-mine the average price of a garage repair over the last two months. E.211 The end of term is approaching and the final tests are drawing near. One student is thinking about improving his average: 1 After four checks, his average was 11 . What was the sum of his marks? 2 His fifth mark is 13 . What’s his new average? 3 With a sixth and final test coming up, he wants to end this term with an average of 12 . What grade should he achieve in this final test? 7. Standard deviations E.204 Here’s a study carried out on the Inter-net, on an auction site. It was carried out on the ages of 3 000 of the site’s most regular customers. Here is the histogram associated with this study : The aim of this exercise is to calculate quartiles, mean and standard deviation. 1 a Complete the following table : Classe C 1 C 2 C 3 C 4 C 5 C 6 C 7 C 8 [13;18[ [18;20[ [20;25[ [25;30[ [30;35[ [35;45[ [45;55[ [55;70[ Effectif Effectif cumulé croissant b Determine median, first and third quartile. 2 We’ll use 27.6 for the value of the mean : a We note x i the middle of the class C i . Fill in the table below : i 1 2 3 4 5 6 7 8 x i b Calculate the mean of this series. 3 a Complete the following table to the nearest unit : i 1 2 3 4 5 6 7 8 x i − x x i − x 2 n i · x i − x 2 b Determine the variance and then the standard devia-tion of this series. https://chingmath.fr chapExoCorrec/5070 sacados/5070 chapExoCorrec/5071 sacados/5071 chapExoCorrec/211 sacados/211 chapExoCorrec/204 sacados/204 1481318815209592555930221355745315521070Age (ans)40 individus
E.4743 A statistical study of a population has produced the following headcount table : Taille 150 ; 160 160 ; 170 170 ; 180 180 ; 190 Effectif 3 23 79 7 All calculations must be given to the nearest hundredth. 1 Calculate the mean of this statistical series from the head-count table. 2 Complete the following table : Classes x i − x ( x i − x ) 2 n i ( x i − x ) 2 [150 ; 160[ [160 ; 170[ [170 ; 180[ [180 ; 190[ 3 Deducting the value of variance : = 1 N k i =1 n i ( x i − x ) 2 4 Give the value of the standard deviation: ff = E.8550 Consider a statistical series in which the value of a characteristic is being studied. Here is the table of numbers associated with this study : Caractère value 5 7 11 13 Effectif 5 2 4 1 1 Determine the mean of this statistical series. 2 a Complete the table below : x i 5 7 11 13 n i 5 2 4 1 x i − x x i − x 2 n i · x i − x 2 b Determine the variance of this statistical series. c Determine the standard deviation of this statistical se-ries. 8. Standard deviations with the calculator E.4766 We measured the size of a group of 10 people listed below : 1.75 m ; 1.64 m ; 1.69 m ; 1.71 m ; 1.79 m 1.64 m ; 1.82 m ; 1.75 m ; 1.63 m ; 1.67 m Using a calculator, determine the mean and standard devia-tion of this statistical series. Results should be rounded to the nearest hundredth. E.4786 At the end of a sports training session, the trainer asks participants to take their pulse. Here’s the data collected in the table below : Pulsation par minute 80 ; 90 90 ; 100 100 ; 110 110 ; 120 Effectifs 3 15 24 18 Using the calculator: 1 Determine the mean of this statistical series rounded to the nearest unit. 2 Determine the standard deviation of this statistical series rounded to the nearest unit. E.4826 A questionnaire was given to students in a first-year class about the number of sports they played each week. The results of this survey gave us the following table of num-bers : Nombre de sports pratiqués 0 1 2 3 Effectif 5 17 6 3 The questions below are to be answered without using the calculators’ statistical functions. The method used must be presented and the results obtained must be rounded to the nearest tenth. 1 Determine the average number of sports played weekly by students in this class. 2 Determine the standard deviation associated with this statistical series. https://chingmath.fr chapExoCorrec/4743 sacados/4743 chapExoCorrec/8550 sacados/8550 chapExoCorrec/4766 sacados/4766 chapExoCorrec/4786 sacados/4786 chapExoCorrec/4826 sacados/4826
E.193 lebanon - June 2005 - 8 points 1000 students from different high schools measured the den-sity of brass using the flask method. The results, rounded to the nearest tenth, are shown in the following table : Masse volumique (en g = cm 3 ) 8 8.1 8.2 8.3 8.4 8.5 8.6 8.7 8.8 8.9 9 9.1 Number 3 19 42 100 200 250 190 113 50 20 7 6 1 Draw a bar chart of this series (graphic units: 1 cm for 0.1 g = cm 3 on the abscissa, graduating from 7.9 g = cm 3 and 1 cm for 20 pupils on the ordinate.) 2 a Determine, specifying your method, the first quar-tile Q 1 , the median m and the third quartile Q 3 of this series. b Draw the box plot for this series, plotting Q 1 , m , Q 3 and the extreme values of the series (unit: 1 cm pour 0.1 g = cm 3 ) c Note I the length of the interquartile range. Calcu-late the percentage of students who measured a density within the range m − I ; m + I 3 a Determine the exact value of the mean — of this se-ries. b Determine the default approximate value to 10 − 3 of the standard deviation ff of this series. c Calculate the percentage of students who measured a density within the range — − 2 ff ; — +2 ff then in the interval — − 3 ff ; — +3 ff E.4749 Here are the 25 grades of ninth graders 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 the calculator, determine the mean and standard deviation of the series. 2 a Complete the staffing table below : Note 0 ; 2 2 ; 4 4 ; 6 6 ; 8 8 ; 10 Effectif Note 10 ; 12 12 ; 14 14 ; 16 16 ; 18 18 ; 20 Effectif b From the headcount table and using your calculator, determine the mean and standard deviation. E.4785 The price of a cinema show at different cinemas in a town was recorded. The data are summarized in the table below : Price (in e ) 7 9 10 Number of cinéma 3 5 2 Without using the calculator’s statistics functions : 1 Determine the mean of this statistical series rounded to the nearest cent. 2 Using the rounded value of the mean, determine the vari-ance and standard deviation of this statistical series (re-sults will be rounded to the nearest hundredth) E.4824 In one school, the marks of 1 er ES A students in the written test of the French bac blanc are given in the table below : Notes 3 5 8 9 11 12 14 16 19 Effectifs 1 3 5 2 3 6 2 4 1 1 Determine, without justification, the mean x and stan-dard deviation ff of this headcount table. (results will be given to the nearest tenth) . 2 The class of 1 er ES B had a standard deviation of 1.7 . Which of these two classes is the more homogeneous? Briefly justify your answer. 3 Show the box plot of the 1 er ES A note series, using for scale 1 cm for 2 points. E.4767 The table of grades for a class is given below : Note 0;4 4;8 8;12 12;16 16;20 Effectif 2 5 10 7 3 Using a calculator, determine the mean and standard devia-tion of this statistical series. Results should be rounded to the nearest hundredth. 9. Medianes E.212 Twenty athletes were measured in cen-timetres : 178 - 176 - 172 - 184 - 182 - 182 - 174 - 176 - 184 - 180 180 - 176 - 180 - 174 - 172 - 176 - 180 - 182 - 176 - 180 1 Calculate the average size of this statistical series (round to the nearest tenth) . 2 a Order the set of sizes found. b Deduce the median value of this statistical series. 3 By grouping the sizes surveyed into classes of 5 cm am-plitude : [170 ; 175[ ; [175 ; 180[ ; [180 ; 185[ ; [185 ; 190[ Construct the associated histogram. https://chingmath.fr chapExoCorrec/193 sacados/193 Liban - Juin 2005 - 8 points chapExoCorrec/4749 sacados/4749 chapExoCorrec/4785 sacados/4785 chapExoCorrec/4824 sacados/4824 chapExoCorrec/4767 sacados/4767 chapExoCorrec/212 sacados/212
0246810012345678 E.215 Teenagers aged 14 to 18 were asked how many times they went to the cinema each month. The bar chart below shows their answers 1 Copy and complete the table below : Nombre de séance par mois 0 1 2 3 4 5 6 7 8 Effectif Effectif. cum. croissant 2 How many movies, on average, does a teenager see per month? (round to the nearest tenth) . 3 Give the range of this statistical series. 4 What is the modal class? 5 Using the line of cumulative increasing numbers : a Determine the median of this statistical series. b Determine the first and third quartile. E.220 1 Here are the marks of four groups of students in the brevet blanc. Complete the boxes for the various indica-tors below : Groupe 1 Groupe 2 Groupe 3 Groupe 4 Notes 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 Scope Median 2 Compare from a qualitative point of view in the light of the indicators calculated previously: a group 1 and group 2 ; b The 2 group and the 4 group ; c The 1 group and the 3 group. E.2017 A survey was conducted among 10th grade students at a school to find out how far they live from their school. Here is a table summarizing this study : Distance (en km ) [0;5[ [5;10[ [10;15[ [15;20[ [20;25[ [25;30[ Frequency (en %) 14 30 25 18 8 5 1 Determine the average distance traveled by a student to reach their school. 2 a Determine the median of this statistical series. b Determine the first and third quartiles. E.1942 1 Here are the marks of four groups of students in the brevet blanc. Complete the boxes for the various indica-tors below : Groupe 1 Groupe 2 Groupe 3 Groupe 4 Notes 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 Scope Median 2 Compare from a qualitative point of view in the light of the indicators calculated previously: a Group 1 and Group 2 b Group 2 and Group 4 c Group 1 and group 3 E.2343 1 Here are the marks of four groups of students in the brevet blanc. Complete the boxes for the various indica-tors below : Groupe 1 Groupe 2 Groupe 3 Groupe 4 Notes 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 Moyenne Etendue Médiane 2 Compare from a qualitative point of view in the light of the indicators calculated previously: a group 1 and group 2 . b The 2 group and the 4 group. c The 1 group and the 3 group. https://chingmath.fr chapExoCorrec/215 sacados/215 0246810012345678 chapExoCorrec/220 sacados/220 chapExoCorrec/2017 sacados/2017 chapExoCorrec/1942 sacados/1942 chapExoCorrec/2343 sacados/2343
02468101214161820102030405060708090100 N N N N E.2342 Here is the table of student marks for the brevet des collèges: Note 0 ; 4 4 ; 8 8 ; 12 12 ; 16 16 ; 20 Number 8 32 61 80 15 Eff. cumulé croissant Freq. cumulé croissant en % 1 What is the modal class of this statistical series? 2 Calculate the establishment’s mean in this examination. (we’ll give the result to the nearest hundredth) . 3 a Complete the line of cumulative increasing numbers, then cumulative increasing frequencies in percent. b Construct, in the frame below, the polygon of cumula-tive increasing frequencies in percent. c Using the polygon of increasing cumulative frequencies in percent, determine the antecedents of 25 % , 50 % and 75 % and interpret these results. 10. Quartiles by count E.2341 On a graduated line, a teacher has ordered the grades of these four classes. Here are their repre-sentations : Series 1: Series 2: Series 3: Series 4: The purpose of the exercise is to divide each of the classes into four parts ˇ of equal size ı representing : The lowest 25 The medium-low quarter The medium-high quarter The strong quarter 1 Plot the median value of the series on each of the gradu-ated lines. 2 Complete the splitting of the series by re-splitting each part in half. 3 Can you give a qualitative judgment of these classes? E.2344 Give the range, median, first and third quartile of the following series : 34 38 39 41 42 43 44 45 45 47 47 48 49 50 51 51 52 52 53 54 55 55 55 55 55 55 55 56 56 57 58 58 58 59 59 59 60 62 62 62 62 63 64 65 66 66 66 66 67 68 68 73 74 74 75 75 79 81 81 85 E.2345 BMI stands for body mass index. In a study of 400 women, here is the table showing the BMI of this population : BMI 19 20 21 22 23 24 25 26 27 28 29 Staff 25 37 106 92 38 39 16 12 15 13 7 Cumulative effects increasing 1 Complete the row for cumulative totals in the table above. 2 Determine the first quartile, median, third quartile, and range of this series. 11. Quartiles by frequencies E.6629 A 2 nd class entry assessment was asked of all these classes : https://chingmath.fr chapExoCorrec/2342 sacados/2342 02468101214161820102030405060708090100 chapExoCorrec/2341 sacados/2341 N N N N chapExoCorrec/2344 sacados/2344 chapExoCorrec/2345 sacados/2345 chapExoCorrec/6629 sacados/6629
15501601651701751801850.10.20.30.40.50.60.70.80.91 02468101214161820Classe 2 - AClasse 2 - BClasse 2 - CClasse 2 - D Note 1 2 3 4 5 6 7 8 9 10 Effectif 15 24 52 80 92 132 154 42 21 2 Eff. cumulé Croissant 15 39 91 171 263 395 549 591 612 614 Freq. cumulé Croissant % 2.4 6.4 14.8 27.9 42.8 64.3 89.4 96.3 99.7 100 1 Here’s the definition of the first quartile of a class : ˇ This is the smallest of the q 1 values of the statistical series such that at least 25 % of its termsis less than or equal to q 1 ı What is the first quartile for this statistical series? 2 Here’s the definition of the third quartile of a class : ˇ This is the smallest of the q 3 values of the statistical series such that at least 75 % of its termsare less than or equal to q 3 ı What is the third quartile for this statistical series? E.2359 We’re looking at the students in a first-year class and studying their height. Here is the statistical series associated with the character height in centimeters : 167 − 181 − 173 − 179 − 165 − 169 − 170 − 174 − 160 172 − 173 − 164 − 170 − 156 − 161 − 171 − 174 − 162 159 − 176 − 170 − 163 − 175 − 155 − 173 − 167 − 168 175 − 170 − 162 − 169 − 170 1 Complete the headcount table below and the associated rows ( frequencies will be given to the nearest 10 − 3 ) . Classe [155;160[ [160;165[ [165;170[ [170;175[ [175;180[ [180;185[ Effectif Fréquence Fréq cum croissante 2 Consider the reference frame below : a Draw the polygon of increasing cumulative frequencies. b Using the polygon of increasing cumulative frequencies, determine the values of the first quartile, median and third quartile. 3 Plot the whisker box corresponding to this statistical se-ries, taking as scale : 1 cm on the graduated line ←→ 2 cm for height. 12. Box plot E.5068 On a graduated line, a teacher has ordered the grades of these four classes. Here are their repre-sentations : 1 Draw the box diagram for each of these classes. 2 Compare these statistical series qualitatively. https://chingmath.fr chapExoCorrec/2359 sacados/2359 15501601651701751801850.10.20.30.40.50.60.70.80.91 chapExoCorrec/5068 sacados/5068 02468101214161820Classe 2 - AClasse 2 - BClasse 2 - CClasse 2 - D
1010.51111.51212.5131881à19001901à19201921à19401941à19601961à1980 192021222324252627282930 E.2366 The Paris Montsouris meteo-rological observatory has been continuously recording outdoor temperatures since 1872 and provides annual averages from these readings. The aim of this exercise is to compare these averages by twenty-year periods between 1880 and 2000. To clarify the vocabulary, we’ll call ˇannual temperatureı the av-erage temperature recorded in a given year (days and nights), expressed in degrees Celsius and rounded to 0.05 o C . Sources Météo France The document below shows box plots constructed from an-nual temperatures during each twenty-year period between 1881 and 1980. On each of these diagrams, the median, first and third quartiles have been plotted. The ends of the ˇmous-tachesı mark the minimum and maximum of this series. For each of the following propositions, indicate whether it is true, false or undecidable (in case the document would not al-low to know whether the proposition is true or false) . Justify the answer. 1 The maximum annual temperature was 12.65 o C for a century, from 1881 to 1980. 2 The annual temperature range was 2.25 o C for one cen-tury, from 1881 to 1980. 3 For a century, from 1881 to 1980, at least thirty years had their annual temperature below 11.5 o C . 4 1961 was the coldest year over the period 1901-1980. E.2368 A survey was carried out on a sample of 1 000 people (600 men and 400 women) in order to study one of the factors predisposing to cardiovascular disease. For each person, we define the body mass index, noted IMC , which is calculated as follows : BMI = P T 2 , where P is the mass (in kg ) and T is the height (in m ) of the person. For a IMC strictly greater than 22 in women and strictly greater than 23 in men, the person is declared ˇ high-risk ı. We represented by the box plot corresponding to the BMI of the 600 men in this study. 1 In this question, we are interested in the statistical series formed by the 600 men in the study. a Give the range, median and quartiles of this series. b Looking at the diagram and justifying each answer, answer true or false to each of the following two state-ments : A : less than 20 % of men are declared ˇat risk élevéı : B : at least 25 % of men are reported as not ˇ at risqueı 2 In this question, we are interested in the IMC of the 400 women in the initial sample. The following table is obtained : IMC 19 20 21 22 23 24 25 26 27 28 29 Numbers 25 37 106 92 38 39 16 12 15 13 7 a Determine the median and quartiles of this series. Us-ing the given scale, draw a box plot for this series b Can we say, from the results, that the percentage of women reported as not ˇ at risk ı is higher than that of men? Justify. https://chingmath.fr chapExoCorrec/2366 sacados/2366 1010.51111.51212.5131881à19001901à19201921à19401941à19601961à1980 chapExoCorrec/2368 sacados/2368 192021222324252627282930
02468101214161820Seconde 1Seconde 2Seconde 3Seconde 4Seconde 5Seconde 6 46810121416182022242628303234cmCBA 024681012141618200.20.40.60.81020 012345678910111213141516171819202o12o22o3 E.2370 Below are the box plots correspond-ing to the 6 second-year classes of a high school during the second-quarter common assessment. 1 Give the scores corresponding to the median, first, third quartile of the Seconde 1 score series. 2 In Seconde 2, can we say that at least one in two students has a mark of 10 or less? Justify. 3 In which Seconde classes can we say that at least 75 % of students have a mark of 13 or below? Justify. 4 For Seconde class 3, give the interquartile range. 5 In Seconde 5, what percentage represents students with a grade of 10 or higher? E.5066 A pétanque boules factory designs competition boules of different masses and diameters. The three masses offered are 700 g , 720 g and 745 g and for each of these masses three diameters are offered : 71 mm , 75 mm , 79 mm A regional champion decides to buy 720 g balls, but hesitates about the diameter. To make his choice. He places a jack at 9 meters, points 200 times with each of the balls of different diameters and measures the distance to the jack. Here are box plots pruned to deciles representing this test. The ends of the diagram are the first and ninth decile respectively. Here are some of the player’s feelings after the test : 1 With the 79 mm ball, I managed some very good throws but also some very bad ones. 2 With the 71 mm ball, I had very good sensations, half my throws were within 16 cm of the jack and I managed some very good ones 3 But my preference is for the 75 mm ball, with which I’m more consistent. Associate the corresponding box diagram with each type of ball. Justify your answer. E.5067 Below is the polygon of increasing cumulative frequencies of grades obtained by a class of 28 students : 1 a Determine the median and quartiles of this statisti-cal series. b Give the value of the inter-quartile range. 2 Draw the box plot associated with this statistical series E.5069 A school has three second-year classes. The box plots below represent their grades on a com-mon assignment : Based on their grade, we also constructed the following three headcount tables : a Note 0;4 4;8 8;12 12;16 16;20 Effectif 4 4 10 3 1 b Note 0;4 4;8 8;12 12;16 16;20 Effectif 3 2 6 8 4 c Note 0;4 4;8 8;12 12;16 16;20 Effectif 6 4 5 5 2 Associate each box plot with the corresponding headcount table. https://chingmath.fr chapExoCorrec/2370 sacados/2370 02468101214161820Seconde 1Seconde 2Seconde 3Seconde 4Seconde 5Seconde 6 chapExoCorrec/5066 sacados/5066 46810121416182022242628303234cmCBA chapExoCorrec/5067 sacados/5067 024681012141618200.20.40.60.81020 chapExoCorrec/5069 sacados/5069 012345678910111213141516171819202o12o22o3
024681012141618201oS-A1oS-B E.2390 Here are the marks obtained by the 1 o S - A in a question on derivatives : 7.5 - 11 - 17 - 12 - 10 - 12 - 5 - 13 - 2.5 9 - 8 - 2 - 9.5 - 7 - 6 - 10 - 17.5 - 18.5 7 - 14 - 13.5 - 6 - 7.5 - 5.5 - 8 - 15.5 - 2.5 1 Complete the staffing table below : Notes [0 ; 4[ [4 ; 8[ [8 ; 10[ [10;12[ [12;16[ [16;20] Effectifs Eff. cumul. croissants 2 Determine in which classes the first quartile, median and third quartile belong respectively. 3 Considering the center of the classes, draw the box plot in the frame below : 4 Answer the following questions : a Quelle (s) classe (s) possède (nt) at least 50 % of its stu-dents with a grade below 9? b Quelle (s) classe (s) possède (nt) at least a quarter of its students with a grade below 7 ? c Give the range and interquartile range for these two classes? d Compare the top quarter of students in each class. 13. Standard deviations E.2361 A statistical study of a population has produced the following headcount table : Taille 150 ; 160 160 ; 170 170 ; 180 180 ; 190 Effectif 3 23 79 7 All calculations should be rounded to the nearest hundredth. 1 Calculate the mean of this statistical series from the head-count table. 2 Complete the following table : Classes x i − x ( x i − x ) 2 n i ( x i − x ) 2 [150 ; 160[ [160 ; 170[ [170 ; 180[ [180 ; 190[ 3 Deducting the value of variance : = 1 N k i =1 n i · ( x i − x ) 2 4 Give the value of the standard deviation: ff = E.7504 By taking the marks for a common mathematics test from all the 1 o S classes in a school,uA sta-tistical study has produced the following table of numbers : Note 0 ; 4 4 ; 8 8 ; 12 12 ; 16 16 ; 20 Effectif 7 21 74 25 13 All calculations should be rounded to the nearest hundredth. 1 Calculate the mean of this statistical series from the head-count table. 2 Complete the following table : Classes x i − x ( x i − x ) 2 n i ( x i − x ) 2 [0 ; 4[ [4 ; 8[ [8 ; 12[ [12 ; 16[ [16 ; 20] 3 Deducting the value of variance : = 1 N k i =1 n i · ( x i − x ) 2 4 Give the value of the standard deviation: ff = 14. Standard deviations with the calculator E.2371 Here are the 25 grades of ninth graders 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 All results will be rounded to the nearest hundredth. https://chingmath.fr chapExoCorrec/2390 sacados/2390 024681012141618201oS-A1oS-B chapExoCorrec/2361 sacados/2361 chapExoCorrec/7504 sacados/7504 chapExoCorrec/2371 sacados/2371
Un concert100500700900110013001500G 010.51111.51212.51313.514102030405060708090100110 1 Using the calculator, determine the mean and standard deviation of the series. 2 a Complete the staffing table below : Note 0;2 2;4 4;6 6;8 8;10 Number Note 10;12 12;14 14;16 16;18 18;20 Number b From the headcount table and using your calculator, determine the mean and standard deviation. E.2367 In one city, a concert hall has pro-grammed 41 concerts during the 2004/2005 season. The results in terms of expected audience numbers are shown in the histogram given in Appendix 3. For example, the man-ager thinks that 6 concerts will attract between 500 and 700 spectators during the 2004/2005 season. 1 Complete the following staffing table : Classe [100;500[ [500;700[ [700;900[ [900;1100[ [1100;1300[ [1300;1500[ Effectif 2 Using a calculator, determine the mean and standard de-viation of this series. Data should be rounded to the nearest tenth. 15. Mean, standard deviation and quartiles E.2391 66 Météo-France weather stations spread across France were used to obtain the annual temper-ature in France for each of the years between 1901 and 2006 . The polygon of increasing cumulative numbers is shown be-low : 1 Using the graph above, determine the values for this sta-tistical series of the first quartile, median and third quar-tile. 2 a Complete the following headcount table : Température moyenne [10;10.5[ [10.5;11[ [11;11.5[ [11.5;12[ Nombre d’année Température moyenne [12;12.5[ [12.5;13[ [13;13.5[ Nombre d’année b Using a calculator, determine the mean and standard deviation of this statistical series rounded to the near-est hundredth. https://chingmath.fr chapExoCorrec/2367 sacados/2367 Un concert100500700900110013001500G chapExoCorrec/2391 sacados/2391 010.51111.51212.51313.514102030405060708090100110
0123450.20.40.60.81 012345 02030405060700.20.40.60.81 E.5132 In a high school, a statistical study looks at the amount of time students spend practicing a per-sonal sport: Durée (en h ) 0 ; 1 2 1 2 ; 1 1 ; 3 2 3 2 ; 2 2 ; 3 3 ; 5 Effectif 152 254 96 61 32 5 1 Using the calculator and without justification, give the mean and standard deviation of this statistical series rounded to the nearest hundredth. 2 a Complete the line of increasing cumulative numbers : Durée (en h ) 0 ; 1 2 1 2 ; 1 1 ; 3 2 3 2 ; 2 2 ; 3 3 ; 5 Effectif cumulés croissante b Determine the classes to which the median and quar-tiles of this statistical series belong. 3 a Complete the frequency and cumulative increasing frequency rows in the table below, rounding values to the nearest hundredth : Durée (en h ) 0 ; 1 2 1 2 ; 1 1 ; 3 2 3 2 ; 2 2 ; 3 3 ; 5 Fréquence Fréquence cumulés croissante b Plot the polygon of increasing cumulative frequencies in the frame below : 4 a Using the polygon of increasing cumulative frequen-cies, determine the value of the median and quartiles of this statistical series. b Show the box plot of this statistical series below : E.5165 1 The senior class B takes the sports test assessment in the javelin throw. Here are the various performances recorded (in meters) : 37 ; 45 ; 61 ; 43 ; 21 ; 19 ; 41 ; 27 52 ; 34 ; 66 ; 35 ; 24 ; 27 ; 51 ; 42 Using a calculator, give the mean and standard devia-tion of this statistical series, rounded to the nearest hun-dredth. 2 It is assumed in this question that the mean of the throws of the students in the senior B class is 39 m and that this class consists of 16 students. At the end of his assessment, the teacher notes that the senior A has an average of 35 m and that the two classes together have an overall average of 36.6 m . Determine the number of students present in the senior class A . 3 When the test was summed up, the results of the four senior classes were collated in the table below : Longueur (en m ) 20 ; 30 30 ; 40 40 ; 50 50 ; 60 60 ; 70 Effectif 5 34 30 18 5 Fréquence Fréquence cumulées croissante a Complete, in the table, the rows of increasing frequen-cies and cumulative frequencies, rounding the results to the nearest hundredth. b In the reference frame below, draw the polygon of in-creasing cumulative frequencies : c Graphically, determine the value of the median and quartiles. (we’ll leave the construction lines present) . 16. Use of the sum https://chingmath.fr chapExoCorrec/5132 sacados/5132 0123450.20.40.60.81 012345 chapExoCorrec/5165 sacados/5165 02030405060700.20.40.60.81
E.2365 Calculate the following sums : a 4 i =1 3 i b 5 i =1 i ( i + 1) c 4 i =1 1 i d 3 i =1 i 2 + 2 i E.2360 Write the following sums using the symbol 1 3 + 6 + 9 + 12 + 15 2 1 + 4 + 9 + 16 + 25 + 36 + 49 3 1 × 2 + 2 × 3 + 3 × 4 + 4 × 5 E.2364 Write the following sums using the operator: A (5 + 1) × 5 2 + (6 + 1) × 6 2 + (7 + 1) × 7 2 b 3 4 + 4 5 + 5 6 + 6 7 + 7 8 c 1 2 + 4 2 + 9 2 + 16 2 + 25 2 + 36 2 17. Unclassified exercises E.1916 Here is the table of student marks for the brevet des collèges: Note 0 ; 4 4 ; 8 8 ; 12 12 ; 16 16 ; 20 Number 5 32 61 80 15 Effectif cumulé Croissant 1 What is the modal class of this statistical series? 2 Calculate the establishment’s mean in this examination. 3 a Complete the line of cumulative increasing numbers. b Construct an orthonormal coordinate system where the scores ( 1 cm = 2 points) and on the ordinates ( 1 cm = 8 pupils) . Show the curve of cumulative increasing numbers in this frame. c Deduce the value of the median. (Construction lines should be left visible) https://chingmath.fr chapExoCorrec/2365 sacados/2365 chapExoCorrec/2360 sacados/2360 chapExoCorrec/2364 sacados/2364 sacados/1916