MIP2602 Assignment 4 (DETAILED ANSWERS) 2024 - DISTINCTION GUARANTEED

MIP2602 Assignment 4 (DETAILED ANSWERS) 2024 - DISTINCTION GUARANTEED - DISTINCTION GUARANTEED - DISTINCTION GUARANTEED Answers, guidelines, workings and references .. Question 1 1.1 Read the scenario below and answer the questions that follow: Mrs Mbeki conducted a survey to find out how many coins the learners in Grade 5 at IMMACULATE CONVENT school had on them (in their pockets or purses). Mrs Mbeki randomly surveyed 40 Grade 5 learners at IMMACULATE CONVENT school. She obtained the following data: 4 6 3 6 7 2 3 3 2 0 0 5 5 4 8 2 0 0 2 1 0 0 0 4 3 5 0 2 3 6 0 5 5 4 8 2 0 0 2 1 1.1.1 What is the random variable of interest in this scenario? (1) 1.1.2 What is the population of interest in this scenario? (1) 1.1.3 What is the sample of interest in this scenario? (1) 1.1.4 Explain the nature of data that was collected in this scenario. In your explanation state whether it is qualitative or quantitative data. Further state whether it is categorical data or numerical data. If the data is numeric, state whether it is discrete or continuous. (3) 1.1.5 Which graph(s) can best display this type of data? Explain your answer. (2) 1.2 The Curriculum and Assessment Policy Statement (CAPS) requires Grade 6 learners to be able to “draw a variety of graphs including pictographs (many-to-one correspondence) to display and interpret data”. Use figure 1 to answer the questions that follow. 4 Figure 1: Cellphones sold in Prayash’s shop 1.2.1 Use figure 1 to answer the following questions: 1.2.1.1 Write down the points that you will use to explain to grade 6 learners what a pictograph is. (2) 1.2.1.2 Draw a pictograph (many-to-one correspondence) to demonstrate what a pictograph looks like. Use =2; = 2; =2; = 2 to represent the data in figure 1. (9) 1.2.2 Which other graph can best represent the data in figure 1? Explain your answer. (2) 1.2.3 Use Microsoft Excel to draw the graph you have mentioned in 1.2.2 using the data in figure 1. (7) 1.2.4 Design (ask) two questions that will help Grade 6 learners interpret the data displayed in figure 1 and the graph you drew for question 1.2.1.2. 1.2.4.1 ____________________________________________. (1) 1.2.4.2 ____________________________________________. (1) [30] Question 2 2.1 In June 2023, the temperatures measured at night (in ◦C) at a weather station in Limpopo were as follows: 12;16;15;12;19;17;27;18;16;14;13;12;12;12;15;16;14;16;15;12;18;16;17;16;15;16;18; 15;16;15;18;19 2.1.1 The researcher wants to analyse the temperatures at a weather station in Limpopo, using the given data, according to given ranges. Complete the table below. MIP2602/102/0/2024 5 Interval of temperatures (in ◦C) Frequency Relative frequency percentage Cumulative relative frequency percentage 12≤x<14 14≤x<16 TOTAL (15) 2.1.1.1 What percentage of temperatures measured at night is less than 16◦C? (1) 2.1.1.2 What percentage of temperatures measured at night is more than 18◦C? (1) 2.1.2 Draw an ordered stem-and-leaf diagram to organise the data in 2.1. (5) 2.1.3 Construct a histogram to represent the temperatures measured at night (in ◦C) at a weather station in Limpopo. Use the frequency table in question 2.1.1 and the class boundaries of 12≤x<14, 14≤x<16 and so on to construct the histogram. (6) 2.1.4 Calculate the following: 2.1.4.1 the mean (correct to three decimal places) (1) 2.1.4.2 the median (1) 2.1.4.3 the mode (1) 2.1.4.4 the variance (correct to three decimal places) (2) 2.1.4.5 the standard deviation (correct to three decimal places) (2) 2.1.4.6 the lower quartile (1) 2.1.4.7 the upper quartile (1) 2.1.5 Is the data symmetrical, positively skewed or negatively skewed? Explain your answer. (2) 2.1.6 Do the data contain (an) outlier(s)? Explain your answer. (5) 2.1.7 Which of the measures of central location will best summarise the data in 2.1? Explain your answer. (2) [46] 6 _______________________________________________________________________ Question 3 3.1 There are 8 pieces of paper in the bag. Two are orange, three are green, two are yellow and one is blue. If you pull a piece of paper from the bag, what is the theoretical probability that the piece will be: Orange ____________________ Green ___________________ Yellow_____________________ Blue _____________________ (4) 3.2 Now, pull a piece of paper from the bag. Use the table to record the colour, and then put the piece back into the bag. Repeat 12 more times. (6) 3.3 According to the results you found in question 3.2, what is the experimental probability of pulling each colour? Orange ____________________ Green ___________________ Yellow_____________________ Blue _____________________ (4) 3.4 How do the theoretical and experimental probabilities compare? _______________________________________________________________________ _______________________________________________________________________ _______________________________________________________________________ (2) MIP2602/102/0/2024 7 3.5 A school’s staff consists of 40 teachers and 8 administrators. There are 5 male administrators and 35 male teachers. Two members of staff are selected at random to attend a meeting. The findings are shown in the following two-way pivot table: Teacher administrator TOTAL Male 35 5 40 Female 5 3 8 Total 40 8 48 What is the probability of each of the following? 3.5.1 A staff member selected at random is an administrator and is a male. (2) 3.5.2 A staff member selected at random is either an administrator or a teacher. (2) 3.5.3 A staff member selected at random is a teacher given that the member of staff is a female. (2) 3.5.4 A staff member selected at a random is either a teacher or is a male or both. (2)