2019 Nov P2 Q2

Written on
November 2020 - Paper 2

Question 1

A Mathematics teacher was curious to establish if her learners' Mathematics marks influenced their Physical Sciences marks. In the table below, the Mathematics and Physical Sciences marks of

15

learners in her class are given as percentages

(\%)

.

$\:$ MATHEMATICS (AS $\%$ )	$26$	$62$	$21$	$33$	$53$	$76$	$32$	$59\:\:$
$\:$ MATHEMATICS (AS $\%$ )	$\:\:43$	$33$	$49$	$51$	$19$	$34$	$85$
$\:$ PHYSICAL SCIENCES (AS $\%$ )	$34$	$67$	$28$	$46$	$65$	$76$	$26$	$73\:\:$
$\:$ PHYSICAL SCIENCES (AS $\%$ )	$\:\:50$	$39$	$57$	$51$	$24$	$41$	$80$

1.1

Determine the equation of the least squares regression line for the data.

(3)

1.2

Draw the least squares regression line on the scatter plot provided in the ANSWER BOOK.

(2)

1.3

Predict the Physical Sciences mark of a learner who achieved

69\%

for Mathematics.

(2)

1.4

Write down the correlation coefficient between the Mathematics and Physical Sciences marks for the data.

(1)

1.5

Comment on the strength of the correlation between the Mathematics and Physical Sciences marks for the data.

(1)

1.6

What trend did the teacher observe between the results of the two subjects?

(1)

\textbf{[10]}

Written on
November 2019 - Paper 2

Question 1

The table below shows the monthly income (in rands) of

6

different people and the amount (in rands) that each person spends on the monthly repayment of a motor vehicle.

$\quad$ MONTHLY INCOME (IN RANDS)	$9\,000$	$13\,500$	$15\,000$	$16\,500$	$17\,000$	$20\,000$
$\quad$ MONTHLY REPAYMENT (IN RANDS)	$2\,000$	$3\,000$	$3\,500$	$5\,200$	$5\,500$	$6\,000$

1.1

Determine the equation of the least squares regression line for the data.

(3)

1.2

If a person earns

R14\,000

per month, predict the monthly repayment that the person could make towards a motor vehicle.

(2)

1.3

Determine the correlation coefficient between the monthly income and the monthly repayment of a motor vehicle.

(1)

1.4

A person who earns

R18\,000

per month has to decide whether to spend

R9\,000

as a monthly repayment of a motor vehicle, or not. If the above information is a true representation of the population data, which of the following would the person most likely decide on:

\quad A

Spend

R9\,000

per month because there is a very strong positive correlation between the amount earned and the monthly repayment.

\quad B

NOT to spend

R9\,000

per month because there is a very weak positive correlation between the amount earned and the monthly repayment.

\quad C

Spend

R9\,000

per month because the point

(18\,000\;;\,9\,000)

lies very near to the least squares regression line.

\quad D

NOT to spend

R9\,000

per month because the point

(18\,000\;;\,9\,000)

lies very far from the least squares regression line.

(2)

\textbf{[8]}

Written on
November 2020 - Paper 2

Question 2

The number of aircraft landing at the King Shaka International Airport and the Port Elizabeth Airport for the period starting in April

2017

and ending in March

2018

, is shown in the double bar graph below.

2.1

The number of aircraft landing at the Port Elizabeth Airport exceeds the number of aircraft landing at the King Shaka International Airport during some months of the given period. During which month is this difference the greatest?

(1)

2.2

The number of aircraft landing at the King Shaka International Airport during these months are:

$\:\:2\,182$	$2\,323$	$2\,267$	$2\,334$	$2\,346$	$2\,175$
$\:\:2\,293$	$2\,263$	$2\,215$	$2\,271$	$2\,018$	$2\,254$

Calculate the mean for the data.

(2)

2.3

Calculate the standard deviation for the number of aircraft landing at the King Shaka International Airport for the given period.

(2)

2.4

Determine the number of months in which the number of aircraft landing at the King Shaka International Airport were within one standard deviation of the mean.

(3)

2.5

Which ONE of the following statements is CORRECT?

\quad A.

During December and January, there were more landings at the Port Elizabeth Airport than at the King Shaka International Airport.

\quad B.

There was a greater variation in the number of aircraft landing at the King Shaka International Airport than at the Port Elizabeth Airport for the given period.

\quad C.

The standard deviation of the number of landings at the Port Elizabeth Airport will be higher than the standard deviation of the number of landings at the King Shaka International Airport.

(1)

\textbf{[9]}

Written on
November 2019 - Paper 2

Question 2

A survey was conducted among

100

people about the amount that they paid on a monthly basis for their cellphone contracts. The person carrying out the survey calculated the estimated mean to be

R\,309

per month. Unfortunately, he lost some of the data thereafter. The partial results of the survey are shown in the frequency table below:

$\quad$ AMOUNT PAID (in Rands)	$\quad$ FREQUENCY
$\quad 0<x \leq 100$	$\quad 7$
$\quad 100<x \leq 200$	$\quad 12$
$\quad 200<x \leq 300$	$\quad a$
$\quad 300<x \leq 400$	$\quad 35$
$\quad 400<x \leq 500$	$\quad b$
$\quad 500<x \leq 600$	$\quad 6$

2.1

How many people paid

R\,200

or less on their monthly cellphone contracts?

(1)

2.2

Use the information above to show that

a=24

and

b=16

.

(5)

2.3

Write down the modal class for the data.

(1)

2.4

On the grid provided in the ANSWER BOOK, draw and ogive (cumulative frequency graph) to represent the data.

(4)

2.5

Determine how many people paid more than

R\,420

per month for their cellphone contracts.

(2)

\textbf{[13]}

Statistics

Question 1

Question 1

Question 2

Question 2