Scatter Diagrams (Copy)
1.
The table shows the number of hours studied and the test score for 6 students:
Hours: 1, 2, 3, 4, 5, 6
Score: 30, 40, 45, 55, 65, 70
Plot a scatter diagram and describe the correlation.
2.
From Q1, draw a line of best fit and estimate the score when hours studied = 7.
3.
The heights (cm) and weights (kg) of 6 students are:
Height: 150, 155, 160, 165, 170, 175
Weight: 45, 50, 52, 55, 60, 63
Plot a scatter diagram. What type of correlation is shown?
4.
From Q3, estimate the weight of a student with height 168 cm using a line of best fit.
5.
The data shows temperature (°C) and number of ice creams sold:
Temp: 15, 18, 20, 22, 25, 28
Sales: 20, 30, 40, 50, 60, 70
Draw a scatter diagram. Describe the correlation.
6.
From Q5, use a line of best fit to predict sales when temp=30°C.
7.
The table shows revision time and exam marks:
Hours: 0, 1, 2, 3, 4
Marks: 20, 30, 40, 55, 65
Is correlation positive, negative, or none?
8.
The number of absences and final grades of students are recorded:
Absences: 0, 2, 4, 6, 8
Grade (%): 90, 80, 70, 60, 50
Plot a scatter diagram. What correlation is seen?
9.
From Q8, estimate the grade if absences=5.
10.
A table shows shoe size and height:
Shoe: 5, 6, 7, 8, 9
Height (cm): 150, 155, 160, 170, 175
Describe the correlation.
11.
In a survey, daily exercise time (minutes) and resting pulse rate are recorded:
Time: 0, 20, 40, 60, 80
Pulse: 90, 80, 75, 70, 65
Describe the correlation.
12.
From Q11, predict the pulse rate if exercise=50 minutes.
13.
The table shows advertising expenditure ($100s) and sales ($1000s):
Ad: 2, 4, 6, 8, 10
Sales: 5, 8, 12, 15, 19
Plot and describe the correlation.
14.
From Q13, estimate sales if advertising = $1200.
15.
The number of hours of sleep and alertness rating (out of 10):
Sleep: 4, 5, 6, 7, 8
Rating: 3, 4, 6, 7, 9
Draw scatter diagram. State correlation.
16.
The age of a car (years) and its resale value ($1000s):
Age: 1, 2, 3, 4, 5
Value: 15, 12, 9, 6, 4
Describe the correlation.
17.
From Q16, estimate the value of a car aged 6 years.
18.
The number of hours students watch TV per week and their exam scores:
Hours: 5, 10, 15, 20, 25
Score: 80, 70, 65, 50, 40
What correlation is shown?
19.
From Q18, predict the score if a student watches 12 hours of TV.
20.
A scatter diagram shows no pattern between shoe size and exam scores. What correlation is this?
21.
The distance travelled (km) and petrol used (litres):
Dist: 50, 100, 150, 200
Petrol: 5, 10, 15, 20
Describe correlation.
22.
From Q21, estimate petrol needed for 250 km.
23.
The hours of revision and exam score for 8 students are:
Hours: 1, 2, 3, 4, 5, 6, 7, 8
Score: 25, 30, 40, 45, 55, 65, 70, 75
Plot scatter and state correlation.
24.
From Q23, estimate score for 9 hours of revision.
25.
A scatter plot shows a roughly straight upward trend but one point far from the line. What is that point called?
26.
The temperature of water and the time taken to freeze:
Temp (°C): −1, −2, −3, −4, −5
Time (mins): 60, 50, 40, 30, 20
What correlation?
27.
From Q26, predict time if water is −6 °C.
28.
The table shows internet usage hours and sleep hours:
Internet: 2, 4, 6, 8, 10
Sleep: 8, 7, 6, 5, 4
State correlation.
29.
From Q28, predict sleep hours if internet=7.
30.
Explain why a line of best fit should not be used to make predictions far outside the data range.
1.
Points (1,30), (2,40), (3,45), (4,55), (5,65), (6,70). Scatter diagram shows upward trend → positive correlation.
2.
Line of best fit drawn through points. At 7 hours → score ≈ 75.
(Extrapolation along straight line).
3.
Height vs weight rises steadily. → strong positive correlation.
4.
At 168 cm, best fit between 165 (55) and 170 (60) → ≈ 58 kg.
5.
As temperature increases, sales increase. → positive correlation.
6.
At 30°C, line of best fit passes ≈ 75 sales.
7.
Higher revision → higher marks. → positive correlation.
8.
Absences ↑, grade ↓. → negative correlation.
9.
At 5 absences, line between 4 (70) and 6 (60). Estimate ≈ 65%.
10.
Shoe size ↑, height ↑. → positive correlation.
11.
More exercise → lower pulse. → negative correlation.
12.
At 50 minutes, line between 40 (75) and 60 (70). Estimate ≈ 73 bpm.
13.
Advertising ↑, sales ↑. → positive correlation.
14.
At $1200 (12 units), between 10 (19) and beyond → estimate ≈ 22,000 sales.
15.
Sleep ↑, alertness ↑. → positive correlation.
16.
Age ↑, value ↓. → negative correlation.
17.
At 6 years, line beyond 5 (4). Estimate ≈ 2–3 ($1000s).
18.
More TV hours → lower scores. → negative correlation.
19.
At 12 hours, between 10 (70) and 15 (65). Estimate ≈ 68.
20.
No relationship → zero correlation.
21.
More distance → more petrol. → perfect positive correlation.
22.
At 250 km, line continues linear. Petrol ≈ 25 L.
23.
Hours vs score rises steadily. → positive correlation.
24.
At 9 hours, line continues beyond 8 (75). Estimate ≈ 80.
25.
Point far from trend line = outlier.
26.
Lower temperature → shorter freezing time. → negative correlation.
27.
At −6°C, line continues → ≈ 10 mins.
28.
Internet ↑, sleep ↓. → negative correlation.
29.
At 7 hours internet, between 6 (6) and 8 (5). Estimate ≈ 5.5 hours sleep.
30.
Because relationships may not remain valid outside observed data → predictions could be unrealistic.