Question

Questions 1,2,3 and 4

With steps please

4. Using data 4.1 Scatter graphs and correlation Ten identical houses had their lofts converted. These scatter graphs show the number of workers, time taken and cost of equipment hire for each loft. Cost of equipment hire () Time taken (weeks) 0310 Number of workers bij Number of workers a Describe the correlation between the number of workers and the time taken. b Describe the correlation between the number of workers and the cost of equipment hire. ci Describe the correlation between the time taken and the cost of equipment hire. ii Sketch a scatter graph to illustrate this correlation. Ten pupils spent between 60 and 90 minutes writing a poem. Each poem was marked out of 100. What correlation would you expect between the time spent writing and the marks obtained? The table shows the incomes of 10 people and the size of their car engines. Income, 10 000 14000 17 000 27 000 30 000 36000 37000 42 000 45 000 50 000 Engine size, cc 1200 1800 1600 1700 2400 3200 1600 2700 3700 2800 a Draw a scatter diagram using these axes. Horizontal axis (income): £10 000 to £50 000 Vertical axis (engine size): 1000 cc to 4000 CC b Describe the correlation between income and engine size. There are three ways of combining the variables x, y, z, in pairs x with y, y with z and z with.x). Write down what sort of correlation each pair will have. The number of people who travel to work by car each month y: The number of people who travel to work by public transport each month The amount of car exhaust pollution each month Illustrate each correlation by sketching a scatter graph. 4.1 Scatter graphs and correlation

Answer 1

Q.1 (a) there is negative correlation between the number of workers & time taken because as the number of workers increases it takes less time to complete the task.

(b) there is positive correlation between Number of workers & cost of equipment line because the more wages is to be paid.

(c) there is negative correlation between the time taken and cost of equipment line.

(d)

800 700 600 500 400 300 200 100 0 2 4 6 8 10 12 Time taken cost of equipment hire

Q.2

As such you have more time to think so you can write more beautiful poem and you can attract more marks so there is a positive correlation between time spend and marks earned.

Q.3

(a)

4000 3500 3000 2500 2000 1500 1000 500 0 0 10000 20000 30000 400 00 50000 60000 INCOME Engine size

(b)

positive slope of the curve shows the positive correlation between income and Engine size

Q.4

Let's make hypothetical table first:-

now make scattered plot diagram for each situation

bus user pollution car user 25 100 700 200 600 30 35 500 300 400 400 40 300 500 45 600 200 50 700 100 60

(I) correlation between x and y

As such there is negative correlation between the number of car users and number of bus user because any person scan use one of these two. So as the number of people using bus increase the car users decrease.

800 700 600 500 400 bus user 300 Linear (bus user) 200 100 0 0 200 400 600 800 Car users bus users

(ii) y and z

As such as the number of bus user increases the car users will be less so the total pollution by car will definitely going to decrease.

60 50 10 0 0 200 400 600 800 bus users 70 40 30 20 pollution by car

(III) x and z

It is a simple logic that as the number of car users increase the polution by car will rise. So there is positive correlation between Number of car users and total polution by car.

60 50 polluti 30 Linear 20 10 0 200 400 600 800 Number of car users 40 polutiom by cars

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