Math L2 Module 13

Mathematics NQF Level 2 Downloaded from hlayiso.com *see terms and conditions Mathematics NQF Level 2

Representing data effectively Module 13 Downloaded from hlayiso.com Mathematics NQF Level 2

Learning activity 13.1 Downloaded from hlayiso.com Mathematics NQF Level 2

3. During a competition participants were asked to guess the height of a toy house measured in matches. The guesses made by a random sample of participants are given below: 298; 315; 385; 362; 322; 318; 322; 336; 342; 333; 351; 315; 322; 336; 341; 328; 342; 360; 322; 306; 327; 333; 311; 308; 344; 318; 355; 335; 329; 356 Draw a stem-and-leaf plot for this data. Downloaded from hlayiso.com Learning activity 13.1

298; 315; 385; 362; 322; 318; 322; 336; 342; 333; 351; 315; 322; 336; 341; 328; 342; 360; 322; 306; 327; 333; 311; 308; 344; 318; 355; 335; 329; 356 Stems Leaves 29 8 30 6 8 31 1 5 5 8 8 32 2 2 2 2 7 8 9 33 3 3 5 6 6 34 1 2 2 4 35 1 5 6 36 0 2 37 38 5 Downloaded from hlayiso.com Learning activity 13.1

Learning activity 13.2 Downloaded from hlayiso.com Mathematics NQF Level 2

The marks obtained in a test out of 20 were as follows: 10; 6; 5; 9; 12; 8; 7; 13; 16; 15; 14; 11; 12; 9; 13; 13; 15; 8; 11; 13; 9; 13; 10; 12; 13 Draw up a tally table and frequency table. Also show the columns for fi X i and the cumulative frequency. Downloaded from hlayiso.com Learning activity 13.2

Marks (Xi) Tally Frequency (fi) fiXi Cumulative frequency 5 | 1 5 1 6 | 1 6 2 7 | 1 7 3 8 || 2 16 5 9 ||| 3 27 8 10 || 2 20 10 11 || 2 22 12 12 ||| 3 36 15 13 |||| | 6 78 21 14 | 1 14 22 15 || 2 30 24 16 | 1 16 25 Total 25 25 277 Downloaded from hlayiso.com Learning activity 13.2

Learning activity 13.3 Downloaded from hlayiso.com Mathematics NQF Level 2

3. The number of fruit shakes sold at a company’s canteen during one week were: Monday = 92; Tuesday = 81; Wednesday = 112; Thursday = 86; Friday = 120; Saturday = 145; Sunday = 130 The number of meat pies sold during the same week were: Monday = 65; Tuesday = 73; Wednesday = 70; Thursday = 62; Friday = 103; Saturday = 120; Sunday = 150Downloaded from hlayiso.com Learning activity 13.3

3.1 Draw up a frequency table. Frequency fruit Frequency meat Day of week shakes pies Monday 92 65 Tuesday 81 73 Wednesday 112 70 Thursday 86 62 Friday 120 103 Saturday 145 120 Sunday 130 150 Downloaded from hlayiso.com Learning activity 13.3

3.2 Draw a compound bar graph. LG Figure 13.3 Downloaded from hlayiso.com Learning activity 13.3

4. The diagram shows the number of people who visited a specific store during a week. Downloaded from hlayiso.com Learning activity 13.3

4.1 What do we call this diagram? A compound bar graph 4.2 How many people visited the store during the week? Total number of people  1 800  600  800  300  700  200  900 400  700  300  1 200  800  1 600  1 200  11 500 Downloaded from hlayiso.com Learning activity 13.3

4.3 How many women visited the store on Friday? 1 200 4.4 Draw a frequency table representing this data. Women Men Day of week frequency frequency Sunday 1 800 600 Monday 800 300 Tuesday 700 200 Wednesday 900 400 Thursday 700 300 Friday 1 200 800 Saturday 1 600 1 200 Downloaded from hlayiso.com Learning activity 13.3

Learning activity 13.4 Module 13 Downloaded from hlayiso.com Mathematics NQF Level 2

2. The following rainfall figures were recorded during one year. They were measured in millimetres (mm) and recorded monthly. Jan. = 150; Feb. = 80; March = 61; April = 35; May = 12; June = 0; July = 0; Aug. = 0; Sept. = 15; Oct. = 25; Nov. = 75; Dec. = 120 Downloaded from hlayiso.com Learning activity 13.4

2.1 Draw a histogram to represent the data. LG Figure 13.5 Downloaded from hlayiso.com Learning activity 13.4

2.2 Would this histogram represent rainfall in Cape Town or Johannesburg? Give a good reason for your answer. Johannesburg, because it lies in a summer rainfall area. Downloaded from hlayiso.com Learning activity 13.4

Learning activity 13.5 Downloaded from hlayiso.com Mathematics NQF Level 2

1. The maximum temperatures (in °C) recorded at 20 weather stations on a specific day were: 12; 9; 14; 5; 18; 26; 27; 16; 18; 22; 14; 22; 28; 17; 10; 22; 21; 20; 12; 23 Downloaded from hlayiso.com Learning activity 13.5

1.1 Draw up a frequency table using six intervals. 23 Total range  28  5 = 6  4 is good choice for class size Average Class interval Tally Frequency interval 5−8 | 1 6,5 9−12 |||| 4 10,5 13−16 ||| 3 14,5 17−20 |||| 4 18,5 21−24 |||| 5 22,5 25−28 ||| 3 26,5 Total 20 Downloaded from hlayiso.com Learning activity 13.5

1.2 Draw a frequency polygon of the data. LG Figure 13.8 Downloaded from hlayiso.com Learning activity 13.5

2. The masses (in kg) of the members of a school chess club are as follows: Boys: 45,4; 55,5; 61,4; 71,3; 40,5; 52,8; 39,9; 47,6; 51,4; 60,3 Girls: 32,4; 39,8; 41,2; 36,5; 43,5; 33,6; 50,8; 42,6; 44,3; 53,6 Downloaded from hlayiso.com Learning activity 13.5

2.1 Draw up a frequency table using six class intervals. 38,9 Total range  71,3  32, 4 = » 6,5 6 Boys Girls Midpoint of Class Tally Frequency class Tally Frequency interval interval 32,1−39,0 35,55 ||| 3 39,1−46,0 ||| 3 42,55 |||| 5 46,01−53,0 ||| 3 49,55 | 1 53,01−60,0 | 1 56,55 | 1 60,01−67,0 || 2 63,55 67,1−74,0 | 1 70,55 Total 10 10 Downloaded from hlayiso.com Learning activity 13.5

2.2 Draw the frequency polygon on the same diagram. LG Figure 13.9 Downloaded from hlayiso.com Learning activity 13.5

Learning activity 13.7 Downloaded from hlayiso.com Mathematics NQF Level 2

1. The nurse took Bogani’s blood pressure every three hours in hospital, starting at 12:00. The results were: 165 170 170 165 155 155 155 ; ; ; ; ; ; 105 100 95 100 90 90 90 Downloaded from hlayiso.com Learning activity 13.7

1.1 Draw a line graph of his blood pressure readings. LG Figure 13.15 Downloaded from hlayiso.com Learning activity 13.7

1.2 When did his blood pressure stabilise? At 24:00 Downloaded from hlayiso.com Learning activity 13.7

Summative assessment Module 13 Downloaded from hlayiso.com Mathematics NQF Level 2

1. A cattle farmer recorded the following births for the first six months of a year: Cows: 3; 1; 5; 6; 2; 7 Bulls: 5; 6; 2; 3; 4; 8 1.1 Draw a compound bar graph. LG Figure 13.17 Downloaded from hlayiso.com Summative assessment – Module 13

1. A cattle farmer recorded the following births for the first six months of a year: Cows: 3; 1; 5; 6; 2; 7 Bulls: 5; 6; 2; 3; 4; 8 1.2 Draw a pie chart diagram for the cows. Jan. Feb. March April May June Total Frequency 3 1 5 6 2 7 24 Cumulative 3 4 9 15 17 24 n = 24 frequency Decimal 0,125 0,042 0,208 0,25 0,083 0,292 1 Angle =f 45° 15,12° 74,88° 90° 29,88° 105,12° 360° 360° × n Percentage 12,5% 4,2% 20,8% 25% 8,3% 29,2% 100% Downloaded from hlayiso.com Summative assessment – Module 13

LG Figure 13.18 Downloaded from hlayiso.com Summative assessment – Module 13

2. Time spent in hours on an assessment activity by 16 girls randomly selected: 1,2; 2,1; 3,1; 2,4; 1,7; 1,2; 2,3; 2,4; 3,1; 3,5; 2,2; 3,2; 2,4; 1,9; 2,8; 2,5 2.1 Draw a histogram of the data Midpoint of class Time spent (h) Tally Frequency interval 1,1−1,5 || 2 1,4 1,6−2,0 || 2 1,8 2,1−2,5 |||| || 7 2,3 2,6−3,0 | 1 2,8 3,1−3,5 |||| 4 3,3 Total 16 Downloaded from hlayiso.com Summative assessment – Module 13

LG Figure 13.19 Downloaded from hlayiso.com Summative assessment – Module 13

2. Time spent in hours on an assessment activity by 16 girls randomly selected: 1,2; 2,1; 3,1; 2,4; 1,7; 1,2; 2,3; 2,4; 3,1; 3,5; 2,2; 3,2; 2,4; 1,9; 2,8; 2,5 2.2 Draw a frequency diagram representing the data. Use five intervals. Downloaded from hlayiso.com LG Figure 13.20 Summative assessment – Module 13

3. Draw a line graph to represent the sales of a car dealer for the first six months of a year if the following vehicle sales were recorded: 15; 20; 18; 22; 13; 25 LG Figure 13.21 Downloaded from hlayiso.com Summative assessment – Module 13

Downloaded from hlayiso.com Mathematics NQF Level 2