NCV 3 Mathematical Literacy - Module 5

Module 5: Communicate information through numbers graphs and tables

Module 5: Communicate information through numbers graphs and tables ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Tackling a statistical problem ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Presenting information ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Collecting information ,[object Object],[object Object],[object Object],[object Object],[object Object]

Accurate terminology and clear questions ,[object Object],[object Object],[object Object],[object Object],[object Object]

Terminology ,[object Object],[object Object],[object Object],[object Object],[object Object]

Questions ,[object Object],[object Object],[object Object]

Activity 1 ,[object Object],[object Object],[object Object],[object Object]

Data collecting tools ,[object Object],[object Object],[object Object],[object Object]

Discrete or continuous ,[object Object],[object Object]

Surveys ,[object Object],[object Object],[object Object],[object Object]

Questionnaires ,[object Object],[object Object],[object Object],[object Object]

Activity 3 ,[object Object],[object Object],[object Object]

Assignment 1 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Samples ,[object Object],[object Object]

Organising the collected information ,[object Object],[object Object]

Western Cape : Area 129 370 square km (10,6 % of total area) Population: 3 633 080 (9% of total population) Population density: 28,1 per square km. Eastern Cape: Area: 169 600 square km Population: 6 436 790 Northern Cape: Area: 361 800 square km Population: 737 310 Orange Free State : Area: 129 480 square km Population 2 726 840 KwaZulu/Natal : Area: 92 180 square km Population: 8 505 340 North-West: Area: 116 190 square km Population: 3 252 990 Gauteng: Area: 18 810 square km Population: 6 869 100 Eastern Transvaal : Area: 78 370 square km Population: 2 921 560 Northern Transvaal : Area: 123 280 square km Population: 5 201 630

Activity 4 ,[object Object],[object Object]

Activity 4 ,[object Object],[object Object],No not really feasible – too much information Yes, but separate pie charts. Bar graph could display more information.

Activity 4 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Gauteng Probably the pie chart and the bar chart because it is easier understand at a glance

Case Study 1 ,[object Object],[object Object]

Case study 1 ,[object Object],[object Object],[object Object],[object Object]

Percentages ,[object Object],[object Object],[object Object],[object Object]

Percentage calculations ,[object Object],[object Object],[object Object],[object Object]

Percentage calculations ,[object Object],[object Object],[object Object],[object Object],[object Object]

Activity 5 ,[object Object],[object Object],[object Object],This learner smoke 17 x 30 cigarettes per month i.e. 510 cigarettes. This amounts to 25,5 packets per month. At an estimated price of R22,50 per packet the monthly expense is 25,5 x 22,5 = R573,75 He is spending 12,72% of his R4500 earned on cigarettes

Activity 5 ,[object Object],[object Object],R1775,70

Activity 6 ,[object Object],[object Object],[object Object],Crispy chips : Cheese curls = 124 : 52 in month 1 and 128 : 52 in month The percentage of cheese curls with respect to “salty” sales = 52÷ 176 x 100 = 70%

Activity 6 ,[object Object],[object Object],[object Object],2650 : 5620 47% of her money spent on food

Activity 7 ,[object Object],[object Object],[object Object],[object Object],[object Object]

Activity 7 ,[object Object],[object Object],[object Object],[object Object],[object Object],Yes, it would keep up with inflation rate – the average wage settlement is given as 9,7% The settlement level He could expect R1925 which is an adaptation of R175 Not probable as the minimum wage is given as R1650 Workers demand a certain percentage increase and employers offer a certain % increase. Negotiations take place and the workers bring their expectation down and the employer raises their % offer until an agreement is reached

Measures of centre ,[object Object],[object Object],[object Object],[object Object],[object Object]

Measures of centre ,[object Object],[object Object],[object Object],[object Object]

Measures of centre ,[object Object],[object Object]

Measures of spread ,[object Object],[object Object],[object Object],[object Object],[object Object]

Measures of spread ,[object Object],[object Object],[object Object],[object Object]

Lower quartile ,[object Object],[object Object],[object Object]

Upper quartile ,[object Object],[object Object],[object Object]

Interquartile range ,[object Object]

For women: Mean = 190 ÷ 15 = 12 Mode= 13 Median= 13 Range= 20 – 5 = 15 Interquartile range: 17 – 9 = 8 For Men: Mean = 270 ÷17 = 15,88 Mode = 17 Median = 17 Range = 22 – 8 = 14 Interquartile range: 20 – 13 = 7 For the A group of data – The mean, mode and median are all close to 13, and the 15 values range from 5 to 20. The interquartile range shows most values to lie between 9 and 17. For the B group of data – The mean, mode and median are all close to 17, and the values range from 8 to 22. The interquartile range shows most values to lie between 13 and 20. The B group seems consistently a bit higher than the A group.

Activity 9 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

The mean = 107390 ÷ 30 = R3579,67 The mode = R2500 (4 occurrences) The median of wages in this factory = R2750 The range of the wages = 15800 – 1800 = R14000 The interquartile range : Quartile 1 = 7,75 position = R2500 Quartile 2 = 23 rd position = R3250 Interquartile range = 3250 - 2500 = 750

Presentation of results ,[object Object],[object Object],[object Object],[object Object]

Line graphs ,[object Object],[object Object]

Scattergraph with line of best fit ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Activity 11 ,[object Object],[object Object],[object Object],a. For the younger age group the trend is downward i.e. the older the child the slower the heartbeat. b. From 30 to 70 years old the trend is upward, i.e. the older you are the faster the heart rate.

Activity 11 ,[object Object],[object Object],[object Object],[object Object],Heart beat is fast just after birth, but becomes slower up to about 20 years old. Thereafter the heartbeat increases slowly but surely year by year. Pulse rate varies throughout the day, is slowest and more comparable just before rising in the morning. Fitness level; recent exercise; stress; health; Genetic disposition; Meals

Bar Chart ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Activity 12 ,[object Object],[object Object],The modal class is two-child families.

Pie Chart ,[object Object],[object Object],[object Object],[object Object]

Most (40%) of children prefer sweetened artificial orange juice, however this is closely followed by pure apple and orange juice mix (35%). Least popular is Milk (25%)

Activity 15 ,[object Object],[object Object],[object Object],[object Object],[object Object],The percentage increase in sale of mobile phones from 2006 to 2007 is 1100million – 160 million increase amount = 940 million sales amount for 2006 . Percentage increase = 17% The probability that a person has a cell phone, globally speaking, is one out of six or 16,67%. For the Motorola company, the $1,2 billion is the negative amount as it represents a loss. The percentage decrease in business swing for Motorola, is 21,47 negative (see table Motorola has 13% of the global market share. This down from owning 26 % therefore the drop was 13%.

Activity 15 ,[object Object],[object Object],[object Object],[object Object],[object Object],“ 112% saturation in cell phone penetration” means that for every 100 people there are 112 cell phones. Samsung’s sale figure on the sub-continent (India) in 2006, has increased by half of 80% which is an increase of 40% on the previous year’s sale. Samsung hopes to sell 200m minus 161m units which is 39m units. The percentage increase in 2008 will then be 39 divided by 161 times 100 = 24,22% The scales of the vertical axes are the same on both graphs and both reach up to 300 million to enable comparisons.

Activity 15 ,[object Object],[object Object],[object Object],[object Object],[object Object],If the conversion factor is : R1 = $0,1247 then $30 = 30 ÷ 0,1247 = R240,58 and $40 = R320,77

Worldwide mobile terminal sales in 2006 & 2007 (thousands of units):

Activity 16 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Activity 16 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Misleading the reader ,[object Object],[object Object],[object Object],[object Object],[object Object]

Activity 19 ,[object Object],Both graphs are correctly plotted and represent the same data with similarly named axes. However, the left hand sketch has a vertical axis commencing incorrectly at 4 and spreading the values over a wider range to let the gain appear large. In the right hand graph the gain appears to be less but the figures are the same.

Activity 19 ,[object Object],Title unclear – the “north” of what? Vertical axis does not start at zero or at least show a break in the axis.

Other errors ,[object Object],[object Object],[object Object]

Probability mathematics ,[object Object],[object Object],[object Object]

Probabilities ,[object Object],[object Object],[object Object],[object Object]

Theoretical probability ,[object Object],[object Object],[object Object]

Activity 19 ,[object Object],Probability possibly not true for “results of an examination” as it depends how much the learner has studied.

Other probability situations ,[object Object],[object Object],[object Object],[object Object],[object Object]

Activity 20 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Odds ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Activity 21 ,[object Object],[object Object],[object Object],Isibomvu which has long odds Vonk which has short odds He will take home 50 x 20 plus the original stake of 50 = R1050

Activity 21 ,[object Object],[object Object],R300 Vonk had been 3 : 2 is the same as 1,5 : 1 and he will win 20 x 1,5 plus 20 = R50

Activity 21 ,[object Object],Probability to throw two heads in a row will be ½ x ½ = ¼ This same calculation follows for each route i.e. for heads followed by tails, for tails followed by heads and for two tails in a row

Activity 21 ,[object Object],4/36 = 1/9 = 0.1111 3/35 = 0.0857

Summative assessment ,[object Object],[object Object]

Summative assessment ,[object Object],[object Object],[object Object],[object Object],[object Object],“ Estimates of the national HIV prevalence for the years 1990 to 1999 show a steady increase from 0,7% to 22,8% in 1998. This indicates a percentage increase of more than 30 times from the beginning of the epidemic.”

Summative assessment ,[object Object],[object Object],[object Object],[object Object],Yes such a person could go to Public Health Services Yearly or annual groups Information was collected at ante-natal clinics Only pregnant women of child-bearing age were used in the survey. In this group it was only the group who went to clinics who were used. The sample is therefore not random but has to be used as very little information is available

Summative assessment ,[object Object]

Summative assessment ,[object Object],[object Object],[object Object],[object Object]

Summative assessment ,[object Object],The total for the first column should read 5 500 and the mean for the last column 52 years average. To be strictly accurate, the HIV prevalence should also read 12.76%

Summative assessment ,[object Object],[object Object],[object Object],It means the percentage of people in that province with HIV. It was fact 22 per cent

Summative assessment ,[object Object],[object Object],[object Object],Percentages Quarters of the year. Mining and Manufacturing

Summative assessment ,[object Object],[object Object],[object Object],[object Object],Management and Education North West By surveying job ads.

NCV 3 Mathematical Literacy - Module 5

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NCV 3 Mathematical Literacy - Module 5