Chapter 8 statistics

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Chapter 8 statistics

  1. 1. Module PMR109 CHAPTER 8 :STATISTICS1.1 Data – a collection of information or facts. Data can be collected by – Counting, Measuring, Observation, Interview or Questionnaires. The data collected should be recorded in Frequency Table by using a tally chart. A tally chart shown below : eg 1 : Tally Chart Mark Tally Marks 48 53 60 65 721.2 Frequency – the number of times a certain number, measurement, score or item occurs. Frequency can be easily obtained by using a tally chart shown by eg 1 and a frequency table is used to organize a set of data. The frequency table can be constructed either vertically or horizontally that shown below. eg 2 : Frequency Table Mark Frequency 48 5 53 7 Mark 48 53 60 65 72 60 4 Frequency 5 7 4 5 3 65 5 72 31.3 The ways to represent and interpret data :A. Pictograms - represents data in the form of a picture diagram, use a picture or a symbol that is easily understood. eg 3 : Group A Group B Group C represents 10 studentsStatistics 109
  2. 2. Module PMR110B. Bar Charts - represents data using vertical or horizontal bars. It is a frequency diagram using rectangles of equal width. eg 4 : School School 160 T140 S120100 R 80 Q 60 40 P 20 0 40 60 80 100 120 140 160 Number of 20 0 Number of Classrooms P Q R S T Classrooms - A dual bar chart can be constructed to represent two sets of data in the same chart by using separate bars or single bar. eg 5 : School School 140 120100 100 80 80 60 60 40 40 20 20 0 0 P Q R Numbe r of P Q R Number of Classrooms Class roomsC. Line Graphs - used to represent changes in data over a period of time. The data is first represented by points. Then line segments are drawn to join the points. eg 6 : Sale of chocolate cakes 100 80 60 40 20 0 Days M T W T F S SStatistics 110
  3. 3. Module PMR111D. Pie chart - a circle, divided into sectors of various sizes, used for illustration and comparison of different categories of data. For a quantity P, the angle of the sector representing P is Frequency of P Angle of sector = × 360° Total frequency = Frequency of P × 360° eg 7 : Type of Food Sold in A Day Fried Rice Curry Noodle Noodle 60o o Soup 40 140o Fried Noodle1.4 Mode, Median and Mean.A Mode – the value or item which occurs most frequently or highest frequency. The mode can determine from a given set of data, a frequency table, a pictogram, a bar chart, a line graph or pie chart. eg8 : 7, 4, 3, 4, 8, 7, 5, 4, 3 mode = 4 ( frequency=3 )B Median – the middle value when all the data are arranged in an increasing or decreasing order. If the number of values is odd, then the median is the middle value. If the number of values is even, then the median is the mean of the two middle values. eg 9a : 10g, 12g, 18g, 10g, 16g eg 9b : 10, 12, 18, 10, 16,14 ⇒ 10, 10, 12, 16, 18 ⇒ 10, 10, 12, 14, 16, 18 Median = 12g Median = (12+14) ÷ 2 = 13 eg 9c : Score 1 2 3 4 5 Frequency 4 6 7 1 3 Total frequency = 4+6+7+1+3 = 21 Median = Number of the 11th score =3 eg 9d : Score 1 2 3 4 5 Frequency 4 6 7 0 3Statistics 111
  4. 4. Module PMR112 Total frequency = 4+6+7+0+3 = 20 Median = Number of the 10th and 11th score 2+3 5 = = = 2.5 2 2C Mean – is the arithmetic average of a set of data. Mean = sum of all the values of data total number of data eg 10a : 5, 2, 6, 3, 4, 6, 5, 2, 3 5+ 2+6+3+ 4+6+5+ 2+3 mean = 9 36 = =4 9 eg 10b : Price (RM) 15 20 25 30 35 Frequency 3 4 2 4 3 (15 × 3) + (20 × 4) + (25 × 2) + (30 × 4)) + (35 × 3) Mean = 3+ 4+ 2+ 4+3 45 + 80 + 50 + 120 + 105 = 16 400 = = RM25 16Example 1: Exercise 1:Day Mon Tue Wed Thu Grade A B C D EAbsentees 10 7 12 13 Frequency 3 8 14 9 6The frequency table shows the The table shows the distribution ofnumber of absentees on four grades obtained by 40 students inparticular school days. Based on the the PMR.information given, find a) How many students obtained either grade A or grade B?a) the day with the highest number of absentees.Solution b) If the grade E is the failing grade,a) Thursday find the number of students who passed.b) the day with the lowest number of absentees.Solution c) Which grade has the highestb) Tuesday frequency?Statistics 112
  5. 5. Module PMR113Example 2 : Number of Tourists to an Island Resort 1999 2000 2001 2002 2003 2004 Represents 2000 touristThe pictogram above shows the number of tourist to an island resort from1999 to 2004.a) Which year had the highest number of tourist?Solution :a) Year 2004b) Find the total number of tourist for the two years which had the same number of tourist.Solution :b) The two years were 2000 and 2002. Total number of tourists for 2000 and 2002 = 2(10x2000) = 40 000c) What was the total number of tourists for the six years?Solution :c) Total number of symbols = 8+10+9+10+4+14 = 55 Total number of tourists = 55 x 2000 = 110 000d) If each tourist spent an average of RM600 during their stay, calculate the total amount of money spent by tourist on the island in 2001.Solution :d) Number of tourists in 2001 = 9 x 2000 = 18 000 Amount spent = 18 000 x 600 = RM 10 800 000Statistics 113
  6. 6. Module PMR114Exercise 2 :MondayTuesdayWednesdayThursdayFriday Represents 60 bowlsThe pictogram shows the number of the bowls of noodles sold in a schoolcanteen from Monday to Friday.a) Which day has the highest sales?b) If the profit from each bowl of noodles sold is RM0.20, find the total profit for the five days.c) Find the difference in the profits obtained from the sales on Monday and Friday.Example 3 : Exercise 3:Sales Figures of Watches for FiveShops Sales of Ice Cream for Six Days Day Sale s Figur e s of Watche s for Fiv e Shops Sat 450 400 Fri 350Numbe r 300 Thursof 250watche s 200 Wed 150 100 Tue 50 Mon A B C D E 0 10 20 30 40 50 60 70 80 90 100 110 120 130 Value (RM) ShopStatistics 114
  7. 7. Module PMR115The vertical bar chart given showsthe sales figures of watches for five a) On which day did he sell theshops in December. most ice cream?a) What was the difference in number of watches sold between the shops with the highest and the lowest sales?Solution :a) Difference = 450 - 175 b) How much more did he sell on = 275 watches Wednesday compare to Monday?b) If Shop E had an increase in sales of 20% the following month, while Shop A sold 30 fewer watches, what was the total sales for the two shops?Solution :b) Shop E : 120% of 400 = 480 watches c) Calculate his total sales for six days. Shop A : 250 – 30 = 220 watches Total sales for the two shops = 480 + 220 = 700 watches d) If his total profit from his ice cream sales was 15%, calculatec) If the average value of a watch the vendor’s profit on Thursday. was RM150, calculate the total value of the watches sold by all five shops in December.Solution :c) Total number of watches = 250+ 175+ 450+ 325+ 400 = 1600 watches Total value = 1600 x 150 = RM240 000The horizontal bar chart aboveshows the sales of an ice creamvendor for six days.Statistics 115
  8. 8. Module PMR116Example 4 : Exercise 4 : M age shs Best 400 m Time s Numbe r of Employe e s in Ne wTe ch 59 Company from 1999 to 2004 58 57 400 56 55 350 54 300 53 Time (sec) 52 250 Numbe r of 51 employe e s 200 50 150 49 48 100 47 50 46 45 0 1999 2000 2001 2002 2003 2004 1999 2000 2001 2002 2003 2004 Ye ar Ye arThe line graph given showsMagesh’s best times for the 400m The line graph above shows thetrack event over a period of 6 years. number of employees in NewTech Company from 1999 to 2004.a) From which year onwards did he run below 55 seconds? a) How many employees were thereSolution : in 1999?a) From 2001 onwards.b) What was his improvement in time after 6 years of training? b) When was there the greatestSolution : increase in the number ofb) Improvement employees ? = Slowest time – Fastest time = 57.5 – 49c) What was his percentage improvement in time from 2002 to c) How many more employees were 2004? there in 2004 compared to 2001?Solution :Difference in time = 52 - 49 = 3 seconds Percentage improvement in time 3 = × 100 % 52 = 5.77%Statistics 116
  9. 9. Module PMR117Example 5 : Exercise 5 : Total Car Sales in Malaysia in 2003 Others tea 56.3° milk Proton 166.7° Perodua cof f ee chocolate Hy undaiAll the Form 3 students took part in a 1survey on their favourite hot drinks. Given that Perodua cars took upThe results were shown in the pie 3chart above. of the nation’s total car sales and Hyundai’s sales was RM21.5 billion.a) Which drink was least preferred by the Form 3 students? a) Find the angle of the sector for i) Perodua cars.Solutions : ii) Hyundai cars.a) Milk was least preferred by Form 3 students.b) Which was the most popular drink among the Form 3 b) How much was the total car sales students? in 2003?Solutions :Tea was the most popular drinkamong the students.c) How many percent of the c) How much was the sales of students like hot chocolate? Proton cars in 2003?Solutions :b) Percentage of students who like hot chocolate = 90o 360o X 100% = 25%Statistics 117
  10. 10. Module PMR118Example 6: used for represent the price ofMr Song bought a basket of the watermelon.watermelons with RM150. He soldthem according to their quantities as d) Find the mean price of theshown in the table below. remaining watermelons, if Mr Price 1.50 2.00 2.50 3.00 Song had only sold 70 fruits with (RM) a collection of RM141. Number 42 12 x 10 of fruits Solution :The total sales for all the d) Number of fruit remainingwatermelons was RM207. = 100 -70 = 30a) Find the value of x.Solution : Mean price of the remaininga) Total sales = 42 x 1.50 + 12 x watermelon : 2.00 + x x 2.50 + 10 x 3.00 207 − 141 207 = 117 +2.5x = 30 2.5 x = 207 – 117 = RM 2.20 x = 90/2.5 = 36 Exercise 6 :b) Find the mean, mode and median of the price of the The table below shows the watermelons. performance of a group of studentsSolution : in a test.b) Total number of fruits = 42+12+36+10 Scores 6 7 8 9 10 = 100 Frequency 2 4 x 5 2 Total collection Mean = Total number of fruits RM 207 a) Given that the modal score is 8 = and the mean score is greater 100 = RM 2.07 than the mode, find the least Mode = RM1.50 possible value for x. Hence, find its mean.  2.00 + 2.00  Median =   .  2  = RM2.00c) Among the mean, mode and median, which is suitable to be b) If another 6 students joined the used for representing the price of group and the scores obtained the watermelons? areSolution : 9, 10, 9, 10, 9, 10c) Mode is not suitable as there are Find the mode, median and 58 fruits costing more than mean of the score. RM1.50. Therefore, mean and median are both suitable to beCommon ErrorsStatistics 118
  11. 11. Module PMR1191. Obtaining information from a pictogram. Group A Group B Represent 50 studentsErrors Correct StepsTotal numbers of students Total numbers of students= 4+6 = ( 4+6) x 50= 10 = 10 x 50 = 5002. Error in determining the mode in a frequency table. Marks 0 1 2 3 4 Frequency 3 4 3 1 5Errors Correct StepsThe mode is 3. The mode is 4.The mode is 5.3. Error in determining the median of a set data.Errors Correct Steps5, 2, 4, 8, 2, 3, 1 (data not rearrange 1, 2, 2, 3, 4, 5, 8in order) Median = 3Median = 84. Salary Less than RM1001 to RM1501 to RM2001 to More than RM1000 RM1500 RM2000 RM2500 RM2500 Frequency 14 118 10 5 4The frequency table above shows the salaries of the staff in Super HomeProducts Company. Find the number of staff whose salaries are less thanRM2000 per month.Errors Correct StepsNumber of staff whose salaries are Number of staff whose salaries areless than RM2000 per month less than RM2000 per month= 14 + 118 = 14 + 118 +10= 132 = 1425. The combined bar chart shows the sales figures for HIQ Bookstore from January to April. Find the total number of non-fiction books sold. Sales Figures from January to Apri l for HI Q bookstore Month Apr. Mar. Feb. Jan 0 20 40 60 80 100 120 140 Number of booksErrorsStatistics 119
  12. 12. Module PMR121Total number of non-fiction books Total number of non-fiction bookssold sold= 100 + 130 + 100 + 110 = 60 + 80 + 70 + 90= 440 = 300Correct Steps5. The table shows the distribution of the scores obtained in tossing a dice 30 times. Find the mean score of each toss. Score 1 2 3 4 5 6 Frequency 5 4 6 8 3 4Errors Correct Steps 1+ 2 + 3 + 4 + 5 + 6 MeanMean = 5+ 4+ 6+8+3+ 4 1(5) + 2(4) + 3(6) + 4(8) + 5(3) + 6(4) = = 0.7 5+ 4+6+8+3+ 4 = 3.4Extra Exercise1 Mode :a. 20 g, 50 g, 30 g, 70 g, 50 g, 40 g, 30 g, 60 g, 50 g, 60 g, 50 g, 60 g Mode = _____ gb. 15 mm, 18 mm, 12 mm, 13 mm, 15mm, 17 mm, 12 mm, 16mm, 15 mm, 13 mm, 14 mm, 15 mm Mode = ______ mmc. 4, 5, 6, 2, 1, 4, 6, 7, 5, 6 Mode =d. Number of matches played 1 2 3 4 5 Frequency 1 4 3 2 3 Mode = _______matchese. Height ( cm ) 120 121 122 123 124 Frequency 2 9 7 3 4 Mode = cmStatistics 121
  13. 13. Module PMR121f. Number Of goals 0 1 2 3 4 Frequency 2 5 4 6 4 Mode = goals2. Mediana. 4, 2, 5, 4, 7, 2, 1 c. 2kg, 4kg, 1kg, 5kg, 4kg, 2kg Median = Median =b. 9, 2, 7, 1, 8, 9, 0 d. 30m, 10m, 30m, 10m, 40m Median = Median =e. Number Of goals 0 1 2 3 4 Frequency 1 5 4 4 3 Total frequency = 1 + 5 + 4 + 4 + 3 = Median = Number of goals of the ___ th Frequency = goalsf. Grade A B C D E Numbers of students 6 12 9 8 11 Total frequency = 6 + 12 + 9 + 8 + 11 = Median =3. Mean ;a. 21, 30, 25, 27, 31, 34 b. 7 ,4 , 6 ,8 ,5 ,7 , 5 Mean = Mean =c. Mass (g) 5 6 7 8 Frequency 5 2 6 7 Mean =Statistics 121
  14. 14. Module PMR1224. The pictogram in Diagram below shows the number of durians sold by three fruits sellers. Calculate the total number of durians sold by three of them. Samad Chong Muthu represents 10 durians5. Sale of chocolate cakes 100 80 60 40 20 0 Days M T W T F S S The line graph shows the sale of chocolate cakes in a week. Find the difference between the highest sales and the lowest sales in the week.6. 70 60 50 40 30 20 10 0 Day M on Tue s We d Thur Fri The line graph shows the number of cars parked at Jeti Lumut over a period of five days. Each car is charged RM 8 per day. What is the total collection for the five days?7 2 1 3 4 6 8 8 7 5 4 5 4 3 1 2 1 1 4 2 4 The data shows the scores obtained by 20 pupils in a game. a) By using the data given, complete the following table. Score 1 2 3 4 5 6 7 8 Frequency b) State the modeStatistics 122
  15. 15. Module PMR1238. The mean of 5, y, 2y, 3y, 12,12, 15, 20 is 11. Find the value of y.9. Calculate the difference between mean and median of the numbers 5, 11, 20, 23, 15, 9, 3, 18.10. Find the difference between mode and median of the numbers 4, 3, 5, 9, 9, 9, 3, 7, 9.11. Given that the mean of 3, 5, 10, 2, x, 15, y is 8, find the value of x+y.12. The pie chart shows the number of coloured balls in a store. Green 8 Purple White 12 6 10 Black Calculate the angle of the sector which represents black balls.13. Diagram below is a line graph which shows the number of residents in a town from 1997 to 2004. a) During which year did the number of residents increase the most? b) How many residents were there in the town at the beginning of 2001? c) Calculate the percentage increase of residents during the year 2002.Statistics 123
  16. 16. Module PMR124Questions based on PMR Format1. The pictogram below shows the number of cars sold by Syarikat Maju Jaya from year 2004 to 2007. 2004 2005 2006 2007 Represents 50 cars. a) Number of cars sold in year 2006 = ______________ b) If 200 cars were sold in year 2005, complete the pictogram above.2. The frequency table below shows the marks obtained by 40 students from form 3 Budiman in the first round of a mathematics quiz. Score 1 2 3 4 5 6 Number of 3 8 5 12 7 5 students a) If students who get more than four marks will go on to the next round, how many students never made to the second round? b) Calculate the percentage of student that can go to the second round.Statistics 124
  17. 17. Module PMR1253. The pie chart below shows the favourite colours chosen by a group of car owners. Tomato Re d 12 Golde n Ye llow 24 Lime Gre e n 8 Sky b lue 16 a) Find the angle of sector for cars with Golden Yellow colour. b) Calculate the percentage of cars with Tomato Red colour.4. The bar chart below shows number of books read by form one, form two and form three students in SMK Sinar Mutiara for the past two months. Nu m b er of books Nilam 2008 35 30 25 20 Sain s 15 English 10 5 0 1 2 3 For m a) Base on the bar chart above, complete the table below. Form 1 2 3 Number of books b) Find the difference between Science and English books read by all students.Statistics 125
  18. 18. Module PMR1265. 21 , 13, 16, 19, 11, 16, 16 Base on the data above, determine: a) the mode b) the median6. The bar chart below shows the population of Kampung Selangkah, Kampung Temai, Kampung Dusun and Kampung Air. Number of resident 400 300 200 m ale fe m ale 100 0 Kam pung Kam pung Kam pung Kam pu ng Se langk ah Te m ai Du sun Air a) Find the total number of male in all the four Kampung. b) Find the percentage of female to the whole population?Statistics 126
  19. 19. Module PMR1277. Class Raden Mayang Bahagia Adil Jujur Iklas Collection(RM) 200 300 50 250 100 310 Based on the table above, complete the bar charts below. (RM) CLASS FUND 350 300 250 200 150 100 50 0 CLASS Rad en Mayan g Bahagia Adil Jujur Iklas8. Number of points 10 20 30 40 50 60 Number of students 5 4 7 5 6 3 The frequency table above shows the marks obtained by a group of students in a marching competition. a) Find the number of students involved in the event. b) Find the mean point from the table.Statistics 127
  20. 20. Module PMR1289. 2001 2002 2003 2004 2005 Represents 25 computers a) The pictograph above shows the sale of computers by Syarikat Indah Computer in five years . Complete the pictograph if the number of computers sold in year 2003 were 100 sets. b) Find the total number of computers sold in five years.10. Number of books 1 2 3 4 5 6 Number of students 2 5 8 3 6 7 The frequency table above shows the number of books read by students in form 3 Bahagia of SMK Pekan under “ PROJEK NILAM”. a) Find the number of students involved in “PROJEK NILAM”. b) Determine the mode.Statistics 128
  21. 21. Module PMR12911. The following data shows the marks obtained by pupils in a mathematic test: 23 27 26 27 22 22 22 23 26 25 24 23 27 27 26 23 22 22 25 25 22 27 26 26 26 25 24 24 23 22 Marks 22 23 24 25 26 27 Frequency a) Complete the frequency table above based on the data given b) Find the mode12. 21, 26, 29, 27, 21, 25, 25, 26, 29, 28, 30, 33, 23,29 a) Find the mode b) Find the median13. The table below shows the marks obtained in an English test. Marks 10 20 30 40 50 Frequency 4 X 15 11 7 a) Given that the number of frequency is 50, find the value of X b) Determine the mode.Statistics 129
  22. 22. Module PMR13014. The Pie chart below shows the subjects most liked by a group of 36 students. Science Geography 120.0º 60.0° History 130.0° Mathematics a) Find the number of students who like science . b) Find the percentage of pupils who like history.15. The horizontal bar chart below shows the number of vehicles sold by three companies A, B and C. CAR VAN C op y Cm a n B A 0 20 40 60 80 No. of ve hicle s Number of Vehiclesa). Calculate the number of vehicles sold by companies A and C.b). Calculate the difference between the number of vans sold by companies B and C.Statistics 130
  23. 23. Module PMR13116. Diagram below is a line graph which shows the number of residents in village X and village Y from 1998 to 2004. Y X a) In which year the difference in the number of residents between village X and village Y is 1 500? b) How many residents are there in village Y in the year 2002? c) Calculate the percentage increase in the number of residents in village X from 2000 to 2002.Statistics 131
  24. 24. Module PMR132PMR past year questions 2004 1. The data in Diagram 5 shows marks obtained by 20 participants in a quiz. 1 4 6 5 4 6 3 5 4 6 2 1 2 4 6 1 2 4 2 3 a) Using the data, complete the frequency table in the answer space. b) State the mode. [3 marks] Answer : a) Marks 1 2 3 4 5 6 Frequency b) 2. Table 1 shows the number of books in the reading corners of three classes. Class Number of Books Aman 75 Bestari 60 Cerdas 90 Table 1 The information for Bestari class is shown fully in the pictograph in the answer space. Complete the pictograph to represent all the information in Table 1. [3 marks] Answer : Number of books in the reading corners Aman Bestari Cerdas Represents _______ booksStatistics 132
  25. 25. Module PMR133 2005 3. Table 1 shows the number of students who play four types of games. Types of games Number of students Ping-pong 8 Badminton 15 Hockey 25 Handball 12 Table 1 The information for badminton is shown fully in the pie chart in the answer space. Complete the pie chart to represent all the information in Table 1. [5 marks] Answer : Badminton 90 °Statistics 133
  26. 26. Module PMR134 2006 4. Table 1 shows the profit made from the sales of nasi lemak at a stall over 5 days. Day Monday Tuesday Wednesday Thursday Friday Profit (RM) 32 40 24 28 28 Table 1 On Diagram 4 in the answer space, draw a line graph to represent all the information in Table 1. Use the scale 2 cm to RM8 on the vertical axis. [5 marks] Answer : Profit (RM ) 40 32 24 16 8 Day Mon Tu e We d Th ur Fr i Diagram 4Statistics 134
  27. 27. Module PMR135 5. Diagram 5 is a pie chart which shows the number of pupils in five group who complete an assignment during a motivational camp. Tuah 10 Jebat x Lekiu Diagram 5 12 Kasturi Lekir 2x 8 It is given that the total number of pupils who complete the assignment is 36. a) Find the value of x. b) Calculate the angle of the sector representing the Tuah group. Show your working. c) State the mode of your data. [5 marks] Answer : a) b) c) 2007 6. Table 1 shows three activities participated by a group of 50 students. Activities Number of students Chess 24 Hockey M Choir 18 Table 1 a) Find the value of M b) Hence , represent all the data by drawing a bar chart in the answer space. [4 marks] Answer : a)Statistics 135
  28. 28. Module PMR136 b) Numbe r of stude nts 28 24 20 16 12 8 4 0 Activ itie s Cheess Hockey Choir 7. Diagram 3 shows the scores obtained by 15 Police Cadets in a shooting competition. 1, 2, 4, 3, 1, 2, 4, 1, 3, 2, 1, 3, 1, 1, 3 Diagram 3 a) Using the data, complete the frequency table in the answer space. b) State the median. [ 3 marks]Statistics 136
  29. 29. Module PMR137 Answer : a) Score Frequency 1 2 3 4 b) Median = 2008 8. Table 15 in the answer space shows the number of gold medals obtained by four schools in a sports competition. The information for school L is shown fully in the pie chart in Diagram 15. Complete a) the angles of the sectors for school M and school N in Table 15. b) the pie chart in Diagram 15 to represent all the information in Table 15. [5 marks] Answer: a) School Number of gold Angle of sector medals K 10 300 L 60 180o M 20 N 30 b) L 180o Diagram 15Statistics 137
  30. 30. Module PMR138 CHAPTER 8 : STATISTICS ANSWERSExercise 1 1f. 3a. 11b. 34 2a. 4c. Grade C 2b. 7 2c. 3Exercise 2 2d. 30ma. Monday 2e. 17, 9 , 2b. RM288 2f. 46, Cc. RM24 3a. 28Exercise 3 3b. 6a. Saturday 3c. 6.75b. RM 45c. RM 530 4. 120d. RM11.25 5. 80Exercise 4a. 25 6. RM2000b. between 2003 and 2004c. 275 7a.Exercise 5 Score 1 2 3 4 5 6 7 8ai. 120o Frequency 4 3 2 5 2 1 1 2aii. 17o 7b. 4b. RM 455.30c. RM 210.80 8. 4Exercise 6. 9. 0a. x= 6 mean= 8.05 10. 2b. mode = 9 median = 9 11. 21 mean = 8.4 12. 100oExtra Exercise1a. 50 13a. 1997 and 20001b. 15 13b. 285001c. 6 11d. 2 13c. 9 111e. 121Statistics 138
  31. 31. Module PMR139Questions based on PMR Format1. a) 250 9. a) Draw 2 symbols correctly b) 4 symbols drawn b) 500 computers2. a) 28 students 10. a) 31 b) 30% b) 33. a) 144º 11. a) 7, 5 ,3, 4, 6, 5 b) 20% b) 224. a) 45, 35, 45 12. a) 29 b) 15 b) 26.55. a) 16 13. a) 13 b) 16 b) 306. a) 650 14. a) 12 students b) 43.48 b) 13.9%7. Draw the bars representing 15. a) 200 Mayang, Adil and Jujur correctly b) 108. a) 30 16. a) year 2001 b) 34 b) 4750 c) 60%PMR Past Year Questions1. a) Marks 1 2 3 4 5 6 Frequency 3 4 2 5 2 4 b) 42. Number of books in the reading corners Aman Bestari Cerdas Represents ___30____ booksStatistics 139
  32. 32. Module PMR1403. Ping Pong Badminton c1 48 ° 90 ° 150° 72 ° Hockey Hand ball4. Profit (RM ) 40 32 24 16 8 Day Mo n Tu e We d Th ur Fr i Diagram 45. a) 2 b) 100o c) LekiuStatistics 140
  33. 33. Module PMR1416. a) 86. b) Numbe r of stude nts 28 24 20 16 12 8 4 0 Activ itie s Cheess Hockey Choir7. a) Score Frequency 1 6 2 3 3 4 4 2 b) 28. a) a) Number of gold School Angle of sector medals K 10 300 L 60 180o M 20 600 N 30 900 b) K 30 ° M ° 60° L ° 180° ° 90° NStatistics 141

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