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NIS Probability and Statistics Diagnostic Test Predict a "likely" or "unlikely" event Q1 Which is the most likely event; a. Snowing in Melbourne in summer b. Rolling a 4 using a dice c. Tossing a head using a coin Construct a bar graph when given data Q2 In my class 5 people have blue eyes, 14 people have brown eyes, 2 people have green eyes and 3 people have hazel coloured eyes. Draw a bar graph to show this information. Correctly use common fraction names Q3 Write the fraction for the following a) one third b) seven eighths c) a quarter Use a number line between 0 and 1 to place common fractions Q4 Mark the fractions on the number line as accurately as you can 0 1 Describe an outcome as "certain", "likely", "unlikely" or "never" Q5 Give one example of each of the following words Certain Likely Unlikely Never Identify equivalent fractions Q6 Which (one or more) of the following fractions is equivalent to two thirds? Circle correct fraction(s) 5 6 1 2 4 6 6 8 6 9 Arrange given simple data into a frequency table Answer questions about the likelihood of an event Q7 A The class was surveyed about how many pets they had and this data was collected 2, 2, 2, 3, 4, 5, 2, 7, 5, 0, 4, 6, 3, 2, 0, 0, 1, 1,2, 0 Complete a frequency table for this data Number Tally B Frequency If you picked a person at random from the class what is the most likely number of pets they would have? Write common fractions with a denominator of 100 Recognise how fractions with a denominator of 100 can be written as a percentage Q8 Write these fractions as percentages 1 = 4 1 = 10 3 = 4 1 = 5 Display the sample space of a single step experiment Q9 A day is to be chosen from a week. List the total sample space. Recognises a set of data as discrete Recognises a set of data as continuous Q10 Write the letter C if the following data is continuous Write the letter D if the data is discrete a) b) c) Shoe sizes of people in my class Distance each person lives from school Number of sisters each person has Associate the link between the number range 0-1 with the language of certain, highly likely, likely, unlikely, highly unlikely and never Q11 Assign a probability as a percentage Assign a probability as a fraction Assign a probability as a decimal Assign a probability in percentage, decimal or fraction format Q12 For the spinner shown below a) What is P(4) as a fraction? b) What is P(3) as a decimal? c) What is P(5) as a percentage? Equivalence between common fractions, decimal and percentages, e.g. 1/2, 0.5 and 50% between 0 and 1 1 Q13 Write these numbers in order of highest to lowest , 20%, 0.6, 0.58 4 Calculates different measures of central location - mean, median and mode Calculate the range of a set of data Q14 A For the data; 2, 3, 4, 2, 5, 2, 1, 1 a) Calculate the mean b) Determine the median c) Determine the mode d) Find the range Interpret mean, median and mode B If I add the number 10 to the data above, circle what happens to each a) b) c) d) Mean Median Mode Range increases increases increases increases stays the same stays the same stays the same stays the same decreases decreases decreases decreases Distinguishes between discrete and continuous data Q15 Circle the type of data each of these is. a) Shoes size Discrete Continuous b) Height Discrete Continuous c) Number of brothers Discrete Continuous Read information off a graph, e.g. bar graph (Discrete data) Draw a simple bar graph given a set of categorical data Q16 Colour Blue Red Green Black Purple Frequency 3 5 3 1 7 Draw a histogram that displays the data in the table above List the sample space of a two-step experiment, e.g. rolling two dice Q17 List the sample space showing all possible outcomes of tossing a coin and rolling a dice Calculates the probability of an outcome, given the sample space, e.g. tree diagram Q18 Calculate the probability of tossing three heads in a row Calculates the probability of an event with replacement Q19 A bag contains 20 red and 20 blue balls. What is the probability of selecting two blue balls taken out at the same time? Interpret a Stem and leaf plot (Continuous data) Q20 The Stem and Leaf Plot below is of the ages of people in a doctor’s waiting room. 02338 1024 236 3 1 15 = 15 a) What fraction of the people are younger than 10? b) Which age is the most frequent? c) What is the median age? Interpret a Histogram (Continuous data) Q21 a) How many people have heights between 159.5 and 169.5 cm? b) In which interval does the mean probably lie? Given a probability, predict how many times an event might occur Q22 How many 5s would you expect to roll if you rolled a dice 600 times? Calculate conditional probability Q23 I travel to work by route A or route B. The probability that I chose route A is 1 2 . The probability that I am late for work if I go via route A is and if I go 4 3 1 via route B the probability that I am late is 3 (a) What is the probability that I am late for work on Monday? (b) Given that I am late for work, what is the probability that I went via route B? Create intervals from ungrouped data Q24 The marks obtained by 40 students in a recent exam are given below: 16, 17, 18, 3, 7, 23, 18, 13, 10, 21, 7, 1, 13, 21, 13, 15, 19, 24, 16, 2, 23, 5, 12, 18, 8, 12, 6, 8, 16, 5, 3, 5, 0, 7, 9, 12, 20, 10, 2, 23 Divide the data into five groups and present the data in a frequency table. Interprets a Box and Whisker Plot representing continuous data Q25 a) What is the range for this box-and-whisker plot? b) What is the median for the above diagram? c) What percentage of weeks where more than 40 TVs sold?