Statistics Past Paper 2021 PDF

**[Section 1]** **Answer all questions in this section** 1. **A pie chart shows the age distribution of persons in some communities who were affected by the covid virus in July. 35% of the people are in the age range "over 50 years". What is the size of the angle representing this gro...

**[Section 1]** **Answer all questions in this section** 1. **A pie chart shows the age distribution of persons in some communities who were affected by the covid virus in July. 35% of the people are in the age range "over 50 years". What is the size of the angle representing this group?** a. **35^o^** b. **90^o^** c. **10^o^** d. **126^o^** 2. **The average weight of four packets is 3kg. The average weight of another six packets is 5 kg. The average weight of all 10 packets is** a. **4 kg** b. **4.5 kg** c. **4.2 kg** d. **5 kg** 3. **The interquartile range of the numbers 0,0,0, 1, 3, 4,7,8 is** a. **2.75** b. **5.5** c. **4** d. **2** Chart, bar chart, histogram Description automatically generated 4. **The bar graph shows how many minutes late Petra was for work last week. On which day did she get to work the earliest?** a. **Monday** b. **Tuesday** c. **Friday** d. **Thursday** ***Use the table to answer questions 5 and 6*** **The table shows the marks of 10 students in the last math test**  5. **What is the median score of Test 1?** a. **79** b. **65** c. **62** d. **63.5** 6. **What is the range of Test 2?** a. **60** b. **51** c. **11** d. **10** 7. **The pie chart shows how Joy used her lunch money last week. What fraction of her money was spent on food?** Diagram Description automatically generated a. [\$\\frac{1}{8}\$]{.math.inline} b. [\$\\frac{1}{3}\$]{.math.inline} c. [\$\\frac{1}{4}\$]{.math.inline} d. [\$\\frac{1}{7}\$]{.math.inline} ***Use the stem and leaf diagram to answer questions 8 and 9***  8. **Which of the following numbers is represented?** a. **12** b. **138** c. **151** d. **142** 9. **The mode of the data is** **a)128** **b) 137** **c) 158** **d) 142** 10. **Look at the number line below, which of the following events has a probability at the marked spot?** A picture containing diagram Description automatically generated a. **Throwing a TAIL on a coin** b. **Not getting a diamond from a pack of playing cards** c. **Saturday following Friday** d. **Scoring a 2 on a dice** 11. **A box contains 2 blue discs, 6 green discs and 10 red discs. If a disc is picked at random what is the probability of getting a green disc?** a. [\$\\frac{6}{10}\$]{.math.inline} b. [\$\\frac{1}{3}\$]{.math.inline} c. [\$\\frac{6}{12}\$]{.math.inline} d. **6**  12. **The table above shows the number of cars passing the school gate last Friday. If 450 cars passed, how many were blue?** a. **36** b. **414** c. **270** d. **180** 13. **A school has 5 year groups. 60 students from the school ate chips at lunch time. The number of chips each pupil ate was recorded. Keith drew this graph. Use the graph to calculate the mean number of chips eaten by the 60 students.** Chart, histogram Description automatically generated a. **346** b. **60** c. **1680** d. **28** 14. **Assume that days are wet or dry. If it is dry on a particular day,** **the probability that it will be dry the next day is 0.4.** **If it is wet on a particular day, the probability that it will** **be wet the next day is 0.7. What is the probability of a** **wet day following a dry day?** a. **0.4** b. **0.7** c. **0.6** d. **0.3** 15. **The diagram shows the possible results when three coins are tossed. The diagram shows** a. **Random sampling** b. **Events** c. **Biased coins** d. **Sample space** 16.  **The graph shows a curve that is** a. **Normally distributed** b. **Positively skewed** c. **Negatively skewed** d. **Symmetric** Chart, histogram Description automatically generated 17. **The data in the histogram above shows the revenues of the top 25 movies in a recent year. How many movies grossed at least \$141 million?** a. **12** b. **10** c. **5** d. **26**  18. **In the normal distribution curve, approximately what percentage of data falls within 2 standard deviations of the mean?** a. **34%** b. **47.5%** c. **95%** d. **5%** ***[Use the table to answer questions 19 and 20]*** Table Description automatically generated **The z-scores of four students in an algebra test are given in the table. The mean** **of the test was 85 and the standard deviation was 4.** 19. **Who had the best score on the test?** a. **Ross** b. **Zack** c. **Natalie** d. **Taylor** 20. **Which of the following statements is true?** a. **All 4 scored more than 85 on the test** b. **Two students scored more than 85 on the test** c. **Three students scored more than 85 on the test** d. **One student scored more than 85 on the test** **[Section II]** **Answer any [three (3) questions] in this section. Each question is worth 10 marks. Show all working where necessary.** **[Question 1]** **The data in the table below is a random sample of the weekly pay rate of 10 working people in two different neighbourhoods** **N 1** **\$7250** **\$11500** **\$7800** **\$8110** **\$8450** **\$7950** **\$7500** **\$8750** **\$9020** **\$8300** --------- ------------- ------------- ------------- ------------- ------------- ------------ ------------- ------------- ------------ ------------- **N 2** **\$12000** **\$7800** **\$11950** **\$10450** **\$10080** **\$9650** **\$10500** **\$10150** **\$9750** **\$12250** A. **Calculate the mean of each data set. Round your answers to the nearest hundred. (5 marks)** B. **Calculate the median of each data set (2 marks)** C. **Calculate the interquartile range of each data set. (3 marks)** **[Question 2]** **Use the following numbers to answer the questions below. For each response, explain how you determined your answer.** **0.1** [\$\\frac{1}{3}\$]{.math.inline} [\$\\frac{10}{11}\$]{.math.inline} **0.05 0.99 0.45** [\$1\\frac{2}{5}\$]{.math.inline} [\$\\frac{7}{15}\$]{.math.inline} **3.5 0.53** A. **Which of the numbers above could represent the probability of an unlikely event? ( 2marks)** B. **Which of the numbers above could represent the probability of an event that is neither unlikely or likely? ( 3 marks)** C. **Which of the numbers above could represent the probability of a likely event? ( 3 marks)** D. **Which of the numbers above could not be probabilities? (2 marks)** **[Question 3]** **A group of boys was asked to name their favourite sport. Their replies are displayed in the bar chart below.**  a. **How many boys were asked? (1 mark)** b. **The information is to be displayed as a pie chart, work out the angle for each sport. (4 marks)** c. **Draw the pie chart to display the information. ( 5 marks)** **[Question 4]** **A class collected data about the number of children in each family. The data is displayed in the bar chart but the last bar is missing.** **Let *n* be the number of families with 5 children.** a. **Show that the total number of** **families is *27 + n* (3 marks)** b. **Write an expression for the total** **number of children (3 marks)** c. **The mean number of children is 3.** **What is the value of *n*?(4 marks)** [Question 5] **In a game, a dice is rolled and a coin is flipped. The score is then worked out using the following rules:** ***If the coin lands on heads, add 2 to the number on the dice*** ***If the coin lands on tails, double the number on the dice*** a. **Complete the table below to show all the possible scores (5 marks)**  b. **What is the probability of scoring more than 5? (2 marks)** c. **State whether you agree or disagree with the following statements and give reasons for your answer each time. (3 marks)** i. **If I accidentally knocked a bottle off the table and onto the floor, there are two possible outcomes; the bottle breaks or the bottle does not break.** **So the probability that it breaks is** [\$\\frac{1}{2}\$]{.math.inline}**.** ii. **In my pack of biscuit, there are five with raisins and seven without; therefore if I pick a biscuit at random, there is a** [\$\\frac{5}{7}\$]{.math.inline} **chance of picking one with raisins.** iii. **To play a board game you must throw a six to start. Patrick says, "I'm unlucky, so I will never be able to start."** [Question 6] Use the following data to complete the questions below. {77, 78, 80, 82, 84, 87, 94,98} a. Find the mean, variance, and standard deviation (6 marks) b. Calculate the z-scores for (4 marks) i. 77 ii. 98