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REVISION ON UNIVARIATED DATA QUESTIONS MULTIPLE-CHOICE (43 MARKS) The following information relates to Questions 1 to 2 Two hundred people were asked about their attitude to compulsory voting (support, no opinion, do not support) and their age (in years). 1 The variables Attitude to compulsory voting and Age are: A both categorical variables B both numerical variables C a categorical and a numerical variable respectively D a numerical and a categorical variable respectively E neither numerical nor categorical variables 2 The most appropriate way to graphically display the information about Age is to use a: A dot plot B bar chart C histogram D segmented bar chart E back-to-back stem plot 3 The variable number of people at a rock concert is a: A a continuous numerical variable B a discrete numerical variable C a continuous categorical variable D a discrete categorical variable E none of the above The following information relates to Questions 4 and 5 The responses of the two hundred people who were asked about their attitude to compulsory voting have been organised into a frequency table as shown below. Some information is missing. Attitude to compulsory voting Support No opinion Frequency Count Percentage 153 10.0 Do not support 27 Total 200 100.0 4 The percentage of people who supported compulsory voting is: A 10.0% B 15.3% C 27.0% D 76.5% E 90.0% 5 The number of people who had no opinion is: A 10 B 15 C 20 D 27 E 200 Questions 6 to 9 relate to the histogram shown below The age distribution for the population of Sassafras in 1986 is shown below 25 percentage 20 15 10 5 0 0 10 20 30 40 50 60 70 80 90 age 6 The percentage of the people in Sassafras who were aged 20 to 29 years in 1986 was closest to: A 9% B 14% C 18% D 20% E 29% 7 The percentage of people in Sassafras who were aged less than 20 years in 1986 was closest to: A 15% B 19% C 20% D 24% E 34% 8 In 1986, 1459 people lived in Sassafras. The number of residents under ten years of age was closest to: A 19 B 146 C 186 D 277 E 729 9 The centre of the distribution lies between: A 10 and 20 B 20 and 30 C 30 and 40 D 40 and 50 E 50 and 60 10 For the distribution displayed by stem plot below, the range is: 3 3 4 4 5 1 5 3 5 4 2 6 3 9 3 3 4 4 4 4 A 3 B 10 C 23 D 25 E 54 11 For the distribution displayed by stem plot below, the centre is: 3 3 4 4 5 A 5 B 6 C 34 1 5 3 5 4 2 6 3 9 3 4 3 4 4 4 D 35 E 36 Questions 12 and 13 relate to the segmented bar chart below The percentage segmented bar chart below shows the distribution of fast food preferences of 200 students. 100 Other 90 80 Pizza Percentage 70 Chinese 60 Fish & chips 50 40 Chicken 30 Hamburgers 20 10 0 Fast food preference 12 The number of students who preferred Pizza is closest to: A 27 B 52 C 66 D 122 E 176 13 For these 200 students, the most popular fast food is: A Chicken B Chinese C Fish & chips D Hamburgers E Pizza 14 The subject choices of VCE students in a large school were recorded. The best graph to display this information would be a: A bar chart B dot plot C histogram D stem plot E back-to-back stem plot The following information relates to Questions15 to 17 The following is a set of test marks: 10, 14, 23, 5, 16, 12, 8, 11, 12, 13, 15 15 The median value is: A 10 B 11 C 12 D 12.5 E 13 16 The first quartile is: A 9 B 10 C 11 D 12 E 12.5 17 The range is: A 5 B 12 C 15 D 18 E 23 The following information relates to Questions 18 to 19 The following is an ordered set of sapling height (in cm): 198, 208, 210, 211, 212, 213, 214, 215, 216, 218 18 The median value is: A 211.5 cm B 212 cm C 212.5 cm D 213 cm E 213.5 cm 19 The interquartile range (IQR) is: A 5 cm B 6 cm C 7 cm D 8 cm E 9 cm 20 The following is a set of 10 daily minimum temperatures (in degrees Celsius): 5, 6, 8, 4, 9, 9, 8, 7, 6, 10 The five-number summary for these temperatures is: A 4, 6, 7.5, 9, 10 B 4, 6, 7, 9, 10 C 4, 6, 8, 9, 10 D 4, 5.5, 7.5, 8.5, 10 E 4, 5.5, 7.5, 8, 10 The following information relates to Questions 21 to 29 A B 1 0 0 5 10 15 20 25 30 35 40 45 50 C 1 0 0 5 10 15 20 25 30 35 40 45 50 0 5 10 15 20 25 30 35 40 45 50 D 1 0 1 0 0 5 10 15 20 25 30 35 40 45 50 0 5 10 15 20 25 30 35 40 45 50 E 1 0 21 The median of box plot D is closest to: A 20 B 25 C 27 D 29 E 30 22 The IQR of box plot B is closest to: A 5 B 10 C 15 D 20 E 44 23 The range of box plot C is closest to: A 5 B 10 C 20 D 25 E 45 24 The description that best matches box plot A is: A symmetric B positively skewed C positively skewed with outliers D negatively skewed E negatively skewed with an outlier 25 The description that best matches box plot B is: A symmetric B negatively skewed with an outlier C negatively skewed D positively skewed E positively skewed with an outlier 26 The description that best matches box plot C is: A symmetric B symmetric with outliers C negatively skewed with outliers D positively skewed E positively skewed with outliers 27 The description that best matches box plot D is: A symmetric B symmetric with outliers C negatively skewed D positively skewed E positively skewed with outliers 28 The description that best matches Box Plot E is: A symmetric B symmetric with outliers C negatively skewed D positively skewed E positively skewed with outliers 29 For Plot C, outliers in the upper tail are defined as data values that are: A greater than 15 B greater than 20 C greater than 25 D greater than 30 E greater than 40 The following information relates to Questions 30 to 31 The following is a set of measurements: 11.0, 11.4, 12.3, 10.5, 11.6, 11.2, 11.8, 11.1, 11.2, 11.3, 11.5 30 The mean value is closest to: A 11.1 B 11.15 C 11.35 D 11.50 E 11.56 31 Correct to two decimal places, the actual value of the standard deviation is: A 0.42 B 0.44 C 0.46 D 0.48 E 0.50 32 The mean of a data distribution is best described as: A the average B the middle value C the central value D the balance point E the middle 50% of values 33 It would not be appropriate to determine the mean and standard deviation of a group of people’s: A salary B thigh length C years of schooling D school type E number of hours worked each week 34 It is reasonable to use the mean measure of the centre of a distribution: A when the distribution is negatively skewed B when the distribution is positively skewed C when the distribution is symmetric D when the distribution is symmetric with outliers E always 35 A student’s mark on a test is 75. The mean mark for their class is 68 and the standard deviation is 4. Their standardised score is: A –2.5 B –1.75 C 0 D 1.75 E 2.5 36 A student’s standardised score on a test is –0.5. The mean mark for their class is 68 and the standard deviation is 4. Their test score is: A 60 B 64 C 66 D 67.5 E 70 In Questions 37 to 40, SD is used as an abbreviation for standard deviation 37 In a normal distribution, approximately 95% of values lie: A within one SD of the mean B within two SDs of the mean C within three SDs of the mean D more than one SD above the mean E more than two SDs below the mean 38 In a normal distribution, approximately 0.3% of values lie: A within one SD of the mean B within two SDs of the mean C within three SDs of the mean D more than three SDs above or below the mean E more than two SDs above or below the mean 39 In a normal distribution, approximately 2.5% of values lie: A within one SD of the mean B within two SDs of the mean C within three SDs of the mean D more than one SD above the mean E more than two SDs above the mean 40 In a normal distribution, approximately 32% of values lie: A within one SD of the mean B within two SDs of the mean C within three SDs of the mean D more than one SD above or below the mean E more than two SDs above or below the mean The following information relates to Questions 41 to 43 The heights of a group of 256 junior athletes is approximately normally distributed with a mean of 157 cm and a standard deviation of 3 cm. 41 The percentage of the junior athletes with heights between 148 and 166 cm is: A 0.03% B 50% C 68% D 95% E 99.7% 42 The number of junior athletes with heights less than 151 cm is around: A 3 B 6 C 12 D 128 E 250 43 The number of junior athletes with heights greater than 154 cm is around: A 82 B 128 C 175 D 215 E 250 Extended-answer questions (90 MARKS) Show answers and any working in the spaces provided. Marks are given for correct and clearly set out working and answers. 1 The five number summary for a set of 33 test scores is: 4, 8, 12, 16, 20. a Write down the range and the interquartile range of the 33 test scores. 2 marks b Use the five number summary to draw a box plot with a suitably scaled and labeled axis. 4 marks 2 The strike rates (runs/100 balls) of 19 one-day cricketers are given below. 70, 63, 59, 66, 54, 69, 64, 72, 61, 54, 85, 59, 58, 57, 58, 69, 91, 58, 61 a Use your calculator to construct an box plot (with outliers) for the data. 2 marks b Use the box plot to locate the median and the quartiles, Q1 and Q3. 2 marks c Complete the following statements: i The middle 50% of the one-day cricketers had a strike rate between ______ runs/100 balls and _____ runs/100 balls. ii 75% of the one-day cricket players had a strike rate greater than _____ runs/100 balls. 2 marks d Write a brief report using the box plot to describe the distribution of the strike rate for these cricketers in terms of shape, centre, spread and outliers. Give appropriate values. 3 marks Total: 30 marks 3 The strike rates (runs/100 balls) of 19 one-day cricketers are given below. 70, 63, 59, 66, 54, 69, 64, 72, 61, 54, 75, 59, 58, 57, 58, 69, 91, 58, 61 a Construct an ordered stem plot with the stems split in two. 3 marks b Describe the shape of the distribution. 2 marks c Determine the modal interval. 1 mark d Determine the percentage of these cricketers with strike rates above 60 runs/100 balls. 2 marks 4 The distribution of ages for the population of Australia in 1986 is shown in the histogram below. Use the histogram to help you complete the report on the distribution of ages in terms of shape, centre and spread. 18 16 percentage 14 12 10 8 6 4 2 0 10 20 30 40 50 age 60 70 80 90 100 Report: The distribution of ages of the population of Australia in 1986 is ____________. There are no outliers. The centre of the age distribution is approximately ____ years. The distribution has a spread of approximately ____ years. 3 marks 5 The lunch choices of 30 students were recorded as ‘W’ for wrap, ‘S’ for salad and ‘P’ for pie, as shown below. S P W S P W W S P P W P P W P S W P P P S W P W W P S S P W a Use the data to complete the table below. Lunch preference Frequency Count Percent Wrap Salad Pie Total 2 marks b Use the table to construct a percentage frequency bar chart for the data. 2 marks 6 The stem plot below shows the distribution of strike rates (runs/100 balls) for 18 one-day cricketers. 5 5 6 6 7 7 8 8 9 Strike rate 4 4 7 8 8 9 9 1 1 3 3 4 6 9 0 2 5 1 a From the shape of the distribution, which measure of centre, the mean or the median, do you think would best indicate the typical strike rate of these cricketers? Explain your decision. 2 marks b Calculate both the mean and median and check your prediction. 2 marks 7 A young athlete competes in three events at her club: the long jump, the high jump and the hop, step and jump. a Complete the table by calculating standard scores for each of her events. Event Long jump High jump Hop, step and jump Distance /height (m) 4.85 1.57 Mean 4.75 1.58 Standard deviation 0.3 0.05 6.45 5.92 0.25 Standardised score 2 marks b Assuming that club member’s performance in each of the three events is approximately normally distributed, in which event did she perform most strongly compared to her club mates and why? 1 mark 8 The amount of time taken by a call centre to process a call is approximately normally distributed with a mean of 3.5 minutes and a standard deviation of one minute. From this information we can conclude that: a 95% of calls will take between ______ and ______ minutes to process b ______ % of calls will take less that 3.5 minutes to process c ______ % of calls will take more than 2.5 minutes to process d ______ % of calls will take more than 6.5 minutes to process e around two thirds of calls will take between ______ and ______ minutes to process f ______ % of calls will take less than 5.5 minutes to process g ______ % of calls will take less than 30 seconds to process h if a calls takes 3 minutes to process, then the call has taken (above/below) ______ the average time to process 8 marks Total: 90 marks Answers Multiple-choice questions 1 C 2 C 3 B 4 D 5 C 6 A 7 E 8 D 9 C 10 C 11 D 12 B 13 D 14 A 15 C 16 B 17 D 18 C 19 A 20 A 21 B 22 D 23 E 24 E 25 D 26 B 27 A 28 E 29 D 30 C 31 C 32 D 33 D 34 C 35 D 36 C 37 B 38 D 39 E 40 D 41 E 42 B 43 D Extended-answer questions 1 a R = 16, IQR = 8 2 marks b 1 0 0 5 10 15 Test score 20 25 4 marks 2 a 2 marks b Q1= 58 , M = 61 , Q3 = 69 2 marks c i 58, 69 ii 58 2 marks d The distribution of strike rates is positively skewed with an outlier. The distribution is centred at 61 runs/100 balls. The spread of the distribution as measured by the IQR is 11 runs/100 balls, and as measured by the range, 37 runs/100 balls. The outlier is a strike rate of 91 runs/100 balls. 3 marks 3 a 5 5 6 6 7 7 8 8 9 4 7 1 6 0 5 4 8 1 9 2 8 3 9 8 4 9 9 1 3 marks b positively skewed with an outlier 2 marks c 55–59 1 mark d 11/19 or 57.9% 2 marks 4 Report: The distribution of ages of the population of Australia in 1986 is positively skewed. There are no outliers. The centre of the age distribution is approximately 30 years. The distribution has a spread of approximately 100 years. 3 marks 5 a Lunch preference Wrap Salad Pie Total Frequency Count 10 7 13 30 Percent 33.3 23.3 43.3 99.9 2 marks b 45 40 30 25 20 e Percentage 35 15 10 5 0 Pie Wrap Lunch preference Salad 2 marks Total: 30 marks 6 a median; positively skewed distribution with possible outliers 2 marks b median = 62 runs/100 balls; mean = 64.7 runs/100 balls (only 2/3rds of the cricketers have strike rates less than the mean). 2 marks 7 a Event Distance Mean Standard deviation Standardised score /height (m) Long jump 3.41 3.22 0.21 0.33 High jump 1.65 1.54 0.05 –0.2 Hop, step and jump 4.23 4.32 0.25 2.1 2 marks b Hop, step and jump; her performance is in the top 2.5% of performances in the club 1 mark 8 a 1.5 and 5.5 minutes b 50% c 84% d 0.15% e 2.5 and 4.5 minutes f 97.5 % g 0.15% h below average 8 marks Total: 90 marks