Math L2 Module 12

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

Data handling Topic 4 Downloaded from hlayiso.com Mathematics NQF Level 2

Calculating the central tendencies and dispersion of data Module 12 Downloaded from hlayiso.com Mathematics NQF Level 2

Learning activity 12.1 Downloaded from hlayiso.com Mathematics NQF Level 2

4. The heights of 12 students (in metres) are: 1,76 1,92 2,01 1,95 1,85 1,79 1,80 1,85 1,83 1,88 1,85 1,83 4.1 Calculate the mean. Mean (x ) 1, 76  1, 92  2, 01  1, 95  1,85  1, 79  1,80  1,85  1,83  1,88  1,85  1,83  12 22,32  12  1,86 Downloaded from hlayiso.com Learning activity 12.1

4. (continued) 4.2 Calculate the median. Arrange in sequential order For median: 1, 76; 1, 79; 1,80; 1,83; 1,83; 1, 85; 1,85; 1, 85; 1,88; 1, 92; 1, 95; 2, 01 1 Median's position  ( n  1) 2 1  (12  1) 2  6, 5 This lies exactly between the 6th and 7th values. Downloaded from hlayiso.com Learning activity 12.1

4. (continued) 4.2 Calculate the median. Arrange in sequential order For median: 1, 76; 1, 79; 1,80; 1,83; 1,83; 1, 85; 1,85; 1, 85; 1,88; 1, 92; 1, 95; 2, 01 6th + 7th values  Median  2 1,85  1,85 Median  2  1,85 Downloaded from hlayiso.com Learning activity 12.1

4. (continued) 4.3 Calculate the mode. 1,76; 1,92; 2,01; 1,95; 1,85; 1,79; 1,80; 1,85; 1,83; 1,88; 1,85; 1,83 Mode = value with the highest frequency Downloaded from hlayiso.com Learning activity 12.1

4. (continued) 4.3 Calculate the mode. 1,76; 1,92; 2,01; 1,95; 1,85; 1,79; 1,80; 1,85; 1,83; 1,88; 1,85; 1,83 Mode = value with the highest frequency  Mode = 1,85 Occurs 3 times Downloaded from hlayiso.com Learning activity 12.1

7. Last year, Thabo’s electricity bill per month was: Jan. = R400; Feb. = R420; March = R400; April = R310; May = R430; June = R500; July = R550; Aug. = R450; Sept. = R440; Oct. = R430; Nov. = R400; Dec. = R500 7.1 Calculate the average account (mean). (x ) 400  420  400  310  430  500  550  450  440  430  400  500  12 5 230  12  R435,83 Downloaded from hlayiso.com Learning activity 12.1

7. Last year, Thabo’s electricity bill per month was: Jan. = R400; Feb. = R420; March = R400; April = R310; May = R430; June = R500; July = R550; Aug. = R450; Sept. = R440; Oct. = R430; Nov. = R400; Dec. = R500 Arrange in sequential order 7.2 Calculate the median. 310; 400; 400; 400; 420; 430; 430; 440; 450; 500; 550; 550 1 6th + 7th values Median's position  ( n  1)  Median  2 2 430  430  6,5  2 Downloaded from hlayiso.com  R430 Learning activity 12.1

7. Last year, Thabo’s electricity bill per month was: Jan. = R400; Feb. = R420; March = R400; April = R310; May = R430; June = R500; July = R550; Aug. = R450; Sept. = R440; Oct. = R430; Nov. = R400; Dec. = R500 7.3 Calculate the mode. Mode = value with the highest frequency Downloaded from hlayiso.com Learning activity 12.1

7. Last year, Thabo’s electricity bill per month was: Jan. = R400; Feb. = R420; March = R400; April = R310; May = R430; June = R500; July = R550; Aug. = R450; Sept. = R440; Oct. = R430; Nov. = R400; Dec. = R500 7.3 Calculate the mode. Mode = value with the highest frequency Mode = R400 Downloaded from hlayiso.com Learning activity 12.1

Learning activity 12.2 Downloaded from hlayiso.com Mathematics NQF Level 2

1. A sample of researchers spent the following times (in hours) finding information per week: 24; 32; 40; 36; 35; 10; 18; 36; 44; 22; 36 Arrange in sequential order 1.1 Calculate the range 10; 18; 22; 24; 32; 35; 36; 36; 36; 40; 44 Range  largest value  smallest value  44  10  34 Downloaded from hlayiso.com Learning activity 12.2

1. A sample of researchers spent the following times (in hours) finding information per week: 24; 32; 40; 36; 35; 10; 18; 36; 44; 22; 36 1.2 Calculate the median 10; 18; 22; 24; 32; 35; 36; 36; 36; 40; 44 n  11 1 1 Median Q 2 position  (n  1)  (11  1)  6 2 2  Q 2  35 Downloaded from hlayiso.com Learning activity 12.2

1. A sample of researchers spent the following times (in hours) finding information per week: 24; 32; 40; 36; 35; 10; 18; 36; 44; 22; 36 1.3 Calculate the lower quartile 10; 18; 22; 24; 32; 35; 36; 36; 36; 40; 44 1 1 Q1 position  ( n  1)  (11  1)  3 4 4  Q1  22 Downloaded from hlayiso.com Learning activity 12.2

1. A sample of researchers spent the following times (in hours) finding information per week: 24; 32; 40; 36; 35; 10; 18; 36; 44; 22; 36 1.4 Calculate the upper quartile 10; 18; 22; 24; 32; 35; 36; 36; 36; 40; 44 3 3 Q3 position  ( n  1)  (11  1)  9 4 4  Q 3  36 Downloaded from hlayiso.com Learning activity 12.2

1. A sample of researchers spent the following times (in hours) finding information per week: 24; 32; 40; 36; 35; 10; 18; 36; 44; 22; 36 1.5 Calculate the interquartile range 10; 18; 22; 24; 32; 35; 36; 36; 36; 40; 44 Q i = Q 3  Q1  36  22  14 Downloaded from hlayiso.com Learning activity 12.2

1. A sample of researchers spent the following times (in hours) finding information per week: 24; 32; 40; 36; 35; 10; 18; 36; 44; 22; 36 1.6 Calculate the semi-interquartile range 10; 18; 22; 24; 32; 35; 36; 36; 36; 40; 44 Q 3  Q1 36  22 Qs =  7 2 2 Downloaded from hlayiso.com Learning activity 12.2

1. A sample of researchers spent the following times (in hours) finding information per week: 24; 32; 40; 36; 35; 10; 18; 36; 44; 22; 36 1.7 Calculate the 75th percentile 10; 18; 22; 24; 32; 35; 36; 36; 36; 40; 44 75th percentile = upper quartile 75th percentile = Q3  36 Downloaded from hlayiso.com Learning activity 12.2

4. The following data shows the gender and height (in cm) of a class: Boys: 199; 199; 192; 190; 188; 186; 184; 184; 182; 182; 181; 180; 179; 179; 179; 178; 178; 175; 169; 169; 169; 168; 168; 159 Girls: 190; 181; 184; 170; 172; 173; 174; 174; 175; 178; 163; 163; 164; 165; 153; 155; 156; 158; 142; 149; 138 Calculate the following measures (i) for the boys and (ii) for the girls: Downloaded from hlayiso.com Learning activity 12.2

4 i) Boys 199; 199; 192; 190; 188; 186; 184; 184; 182; 182; 181; 180; 179; 179; 179; 178; 178; 175; 169; 169; 169; 168; 168; 159 4.1 number of students n  24  24 boys Downloaded from hlayiso.com Learning activity 12.2

4 i) Boys 159; 168; 168; 169; 169; 169; 175; 178; 178; 179; 179; 179; 180; 181; 182; 182; 184; 184; 186; 188; 190; 192; 199; 199 Put in sequential order 4.2 median 1 1 Q 2 position  (n  1)  (24  1)  12,5 2 2 12th + 13th values 179  180  Q2    179,5 2 2 Downloaded from hlayiso.com Learning activity 12.2

4 i) Boys 159; 168; 168; 169; 169; 169; 175; 178; 178; 179; 179; 179; 180; 181; 182; 182; 184; 184; 186; 188; 190; 192; 199; 199 In sequential order 4.3 range Range  largest  smallest = 199  159  40 Downloaded from hlayiso.com Learning activity 12.2

4 i) Boys 159; 168; 168; 169; 169; 169; 175; 178; 178; 179; 179; 179; 180; 181; 182; 182; 184; 184; 186; 188; 190; 192; 199; 199 In sequential order 4.4 lower quartile Q1 position  1 (n  1)  1 (24  1)  6, 25 4 4  Q1  169  0, 25 (175  169)  169  1,5  170,5 Downloaded from hlayiso.com Learning activity 12.2

4 i) Boys 159; 168; 168; 169; 169; 169; 175; 178; 178; 179; 179; 179; 180; 181; 182; 182; 184; 184; 186; 188; 190; 192; 199; 199 In sequential order 4.5 upper quartile 3 3 Q3 position  ( n  1)  (24  1)  18, 75 4 4  Q3  184 0,75 (186  184)  184  1,5  185, 5 Downloaded from hlayiso.com Learning activity 12.2

4 i) Boys 159; 168; 168; 169; 169; 169; 175; 178; 178; 179; 179; 179; 180; 181; 182; 182; 184; 184; 186; 188; 190; 192; 199; 199 In sequential order 4.6 interquartile range Q i  Q 3  Q1  185, 5  170, 5  15 Downloaded from hlayiso.com Learning activity 12.2

4 i) Boys 159; 168; 168; 169; 169; 169; 175; 178; 178; 179; 179; 179; 180; 181; 182; 182; 184; 184; 186; 188; 190; 192; 199; 19 In sequential order 4.7 semi-interquartile range Qi Qs  2 15  2  7,5 Downloaded from hlayiso.com Learning activity 12.2

4 ii) Girls 190; 181; 184; 170; 172; 173; 174; 174; 175; 178; 163; 163; 164; 165; 153; 155; 156; 158; 142; 149; 138 4.1 number of students n  21  21 girls Downloaded from hlayiso.com Learning activity 12.2

4 ii) Girls 138; 142; 149; 153; 155; 156; 158; 163; 163; 164; 165; 170; 172; 173; 174; 174; 175; 178; 181; 184; 190 In sequential order 4.2 median 1 1 Q 2 position  (n  1)  (21  1)  11 2 2  Q 2  11th value  165 Downloaded from hlayiso.com Learning activity 12.2

4 ii) Girls 138; 142; 149; 153; 155; 156; 158; 163; 163; 164; 165; 170; 172; 173; 174; 174; 175; 178; 181; 184; 190 In sequential order 4.3 range Range  largest  smallest = 190  138  52 Downloaded from hlayiso.com Learning activity 12.2

4 ii) Girls 138; 142; 149; 153; 155; 156; 158; 163; 163; 164; 165; 170; 172; 173; 174; 174; 175; 178; 181; 184; 190 In sequential order 4.4 lower quartile 1 1 Q1 position  (n  1)  (21  1)  5,5 4 4  Q1  155  0,5 (156  155)  155  0,5  155,5 Downloaded from hlayiso.com Learning activity 12.2

4 ii) Girls 138; 142; 149; 153; 155; 156; 158; 163; 163; 164; 165; 170; 172; 173; 174; 174; 175; 178; 181; 184; 190 In sequential order 4.5 upper quartile 3 3 Q3 position  (n  1)  (21  1)  16,5 4 4  Q3  174  0, 5(175  174)  174  0,5  174, 5 Downloaded from hlayiso.com Learning activity 12.2

ii) Girls 138; 142; 149; 153; 155; 156; 158; 163; 163; 164; 165; 170; 172; 173; 174; 174; 175; 178; 181; 184; 190 In sequential order 4.6 interquartile range Q i  Q 3  Q1  174,5  155,5  19 Downloaded from hlayiso.com Learning activity 12.2

ii) Girls 138; 142; 149; 153; 155; 156; 158; 163; 163; 164; 165; 170; 172; 173; 174; 174; 175; 178; 181; 184; 190 In sequential order 4.7 semi-interquartile range Qi Qs  2 19  2  9,5 Downloaded from hlayiso.com Learning activity 12.2

Summative assessment Module 12 Downloaded from hlayiso.com Mathematics NQF Level 2

1. Use the ungrouped data: Boys’ masses in kg: 82; 41; 62; 51; 63; 55; 53; 62 Girls’ masses in kg: 35; 39; 43; 62; 51; 49; 47; 50; 53 Calculate the mean: Boys: x  41  51  53  55  62  62  63  82 8  58, 625 35  39  43  47  49  50  51  53  62 Girls: x 9  47, 667 Downloaded from hlayiso.com Summative assessment – Module 12

1. Use the ungrouped data: Boys’ masses in kg: 82; 41; 62; 51; 63; 55; 53; 62 Girls’ masses in kg: 35; 39; 43; 62; 51; 49; 47; 50; 53 Calculate the median: Boys: 41; 51; 53; 55; 62; 62; 63; 82 In sequential order Q 2 position  1 (n  1)  Median  55  62 2 2 1  58,5  (8  1) 2  4,5 Downloaded from hlayiso.com Summative assessment – Module 12

1. Use the ungrouped data: Boys’ masses in kg: 82; 41; 62; 51; 63; 55; 53; 62 Girls’ masses in kg: 35; 39; 43; 62; 51; 49; 47; 50; 53 Calculate the median: Girls: 35; 39; 43; 47; 49; 50; 51; 53; 62 In sequential order 1 Q 2 position  ( n  1)  Median  49 2 1  (9  1) 2 5 Downloaded from hlayiso.com Summative assessment – Module 12

1. Use the ungrouped data: Boys’ masses in kg: 82; 41; 62; 51; 63; 55; 53; 62 Girls’ masses in kg: 35; 39; 43; 62; 51; 49; 47; 50; 53 Calculate the mode: Boys: 41; 51; 53; 55; 62; 62; 63; 82 In sequential order  Mode  62 Girls: 35; 39; 43; 47; 49; 50; 51; 53; 62 In sequential order  No mode Downloaded from hlayiso.com Summative assessment – Module 12

2. A supermarket sold bread during one white week and it was recorded as brown from Monday to Sunday: 100 94 125 115 120 82 135 ; ; ; ; ; ; 120 110 135 135 150 105 155 Downloaded from hlayiso.com Summative assessment – Module 12

2. (continued) Calculate the mean: 82  94 100 105 110 115 120 120 125 135 135 135 150 155  14 1 681  14  120,1  120 Downloaded from hlayiso.com Summative assessment – Module 12

2. (continued) Calculate the median: In sequential order 82; 94; 100; 105; 110; 115; 120; 120; 125; 135; 135; 135; 150; 155 1 120  120 Median's position  (n  1)  Median  2 2 1  (14  1)  120 2  7,5 Downloaded from hlayiso.com Summative assessment – Module 12

2. (continued) Calculate the mode: 82; 94; 100; 105; 110; 115; 120; 120; 125; 135; 135; 135; 150; 155 Mode  135 Downloaded from hlayiso.com Summative assessment – Module 12

Click above to play this video. Downloaded from hlayiso.com Summative assessment – Module 12

Click above to play this video. Downloaded from hlayiso.com Summative assessment – Module 12

Click above to play this video. Downloaded from hlayiso.com Summative assessment – Module 12

Click above to play this video. Downloaded from hlayiso.com Summative assessment – Module 12

Click above to play this video. Downloaded from hlayiso.com Summative assessment – Module 12

Downloaded from hlayiso.com Mathematics NQF Level 2