Maths Level 4 Module 12

Mathematics NQF Level 4 *see terms and conditions Downloaded from hlayiso.com Mathematics NQF Level 4

Data handling and probability models Topic 4 Downloaded from hlayiso.com Mathematics NQF Level 4

Use variance and regression analysis to interpolate and extrapolate bivariate data Model 12 Downloaded from hlayiso.com Mathematics NQF Level 4

Learning activity 12.3 Downloaded from hlayiso.com Mathematics NQF Level 4

Scatter plot vid 21 Downloaded from hlayiso.com Learning activity 12.3

Learning activity 12.5 Downloaded from hlayiso.com Mathematics NQF Level 4

Least squares progression vid 22 Downloaded from hlayiso.com Learning activity 12.5

1) The numbers of cars passing an observation point every 5 minutes during an hour are as follows: 120; 200; 320; 350; 220; 200; 120; 100; 80; 60; 50; 40 Calculate the following: 1.1) Mean 40 + 50 + 60 + 80 + 100 + 120 + 120 + 200 + 200 + 220 + 320 + 350 x= 12 1860 = 12 x = 155 Downloaded from hlayiso.com Summative assessment – Module 12

1.2) Standard deviation Mark (x) Deviation from mean or Mark (x) x2 (x − x ) ( x − x )2 40 40 − 155 = −115 13 225 40 1 600 50 50 − 155 = −105 11 025 50 2 500 60 60 − 155 = −95 9 025 60 3 600 80 80 − 166 = −75 5 625 80 6 400 100 100 − 155 = −55 3 025 100 10 000 120 120 − 155 = −35 1 225 120 14 400 120 120 − 155 = −35 1 225 120 14 400 200 200 − 155 = 45 2 025 200 40 000 200 200 − 155 = 45 2 025 200 40 000 220 220 − 155 = 65 4 225 220 48 400 320 320 − 155 = 165 27 225 320 102 400 350 350 − 155 = 195 38 025 350 122 500 0 117 900 1 860 ∑ x 2 = ∑x= 406 200 Downloaded from hlayiso.com Summative assessment – Module 12

1.2) Continued Σ( x − x ) 2 1 Variance = σ = nΣ x 2 − ( Σ x ) 2 N n OR 1 117 = 900 12(406 200) − (1 860) 2 = 12 12 1 = = 9 825 4 874 400 − 3 459 000 12 σ = 9825 = 99,12 σ = 99,12 Downloaded from hlayiso.com Summative assessment – Module 12

2) Peter scored the following marks out of 10 for ten tests in Mathematics: 4; 8; 3; 7; 5; 4; 6; 2; 9; 4 Calculate the following: 2.1) mean 2+3+ 4+ 4+ 4+5+ 6+ 7 +8+9 x= 10 52 = 10 = 5, 2 Downloaded from hlayiso.com Summative assessment – Module 12

2.2) Standard deviation Mark (x) Deviation from mean or Mark (x) x2 (x − x ) ( x − x )2 2 2 − 5,2 = −3,2 10,24 2 4 3 3 − 5,2 = −2,2 4,84 3 9 4 4 − 5,2 = −1,2 1,44 4 16 4 4 − 5,2 = −1,2 1,44 4 16 4 4 − 5,2 = −1,2 1,44 4 16 5 5 − 5,2 = −0,2 0,04 5 25 6 6 − 5,2 = 0,8 0,64 6 36 7 7 − 5,2 = 1,8 3,24 7 49 8 8 − 5,2 = 2,8 7,84 8 64 9 9 − 5,2 = 3,8 14,44 9 81 0 45,6 ∑x=52 ∑ x2 = 316 Downloaded from hlayiso.com Summative assessment – Module 12

2.2) Continued Σ( x − x ) 2 1 Variance = OR σ = n Σ x 2 − ( Σ x ) 2 n n 45, 6 1 = = 10(316) − (52) 2 10 10 = 4,56 1 = 3160 − 2704 σ = 4.56 10 σ = 2,135 = 2,135 Downloaded from hlayiso.com Summative assessment – Module 12

3) The relationship between the height of a sample of male students and their shoe size is given below. Draw a scatter plot of the data. Height in 1,70 1,75 1,77 1,80 1,80 1,81 1,85 1,89 1,90 1,92 metres Shoe size 7 8 9 8 10 9 11 10 11 12 Downloaded from hlayiso.com Summative assessment – Module 12

3) Continued Figure 12.18 Downloaded from hlayiso.com Summative assessment – Module 12

4) Draw the intuitive line of best fit for the following data: x 1 2 3 4 5 6 7 8 9 y 9 8,1 7 5,8 4,9 6 6,9 2,2 1 Downloaded from hlayiso.com Figure 12.19 Summative assessment – Module 12

5) The following table shows the braking distance and speed in an experiment: Speed km/h (x) 60 80 100 120 140 Braking distance m (y) 32 33 49 64 72 5.1 Determine the equation of the least squares regression line. Speed Braking x − x y − y ( x − x )( y − y ) ( x − x ) 2 km/h distance m (y) 60 32 −40 −20,2 808 1 600 80 44 −20 −8,2 164 400 100 49 0 −3,2 0 0 120 64 20 11,8 236 400 140 72 40 19,8 792 1 600 Sum 500 261 0 0 2 000 4 000 Mean x = 100 Downloaded y = 52,2 from hlayiso.com Summative assessment – Module 12

5.1 Continued Σ( x − x )( y − y ) y= a + bx b= Σ( x − x ) 2 52, 2= a + 0,5(100) 2 000 = 4 000 =a 52, 2 − 50 = 0,5 = −2, 2 yˆ = −2, 2 + 0,5 x Downloaded from hlayiso.com Summative assessment – Module 12

5.2) Represent the data in a scatter plot. Figure 12.20 Downloaded from hlayiso.com Summative assessment – Module 12

5.3) Use the regression line to predict the braking distance in metres when the speed is 160 km/h. 82,2 km from A Downloaded from hlayiso.com Summative assessment – Module 12

Mathematics NQF Level 2 Downloaded from hlayiso.com Mathematics NQF Level 4