Exam-Style Problems

Stage 9 - Q1 - 4 marks

20247

Draw a frequency polygon for the table. Use class midpoints and label both axes.

Time (min)

Frequency

\(10\le t<20\)

4

\(20\le t<30\)

8

\(30\le t<40\)

13

\(40\le t<50\)

5

\(50\le t<60\)

3

Hint

Find the middle of each interval before plotting.

Stage 9 - Q2 - 4 marks

20248

Two equal-sized samples record completion time. Compare how many times are at least 50 minutes. Which sample has more slower completions by this criterion?

Frequency

20

30

40

50

60

70

0

5

10

15

Time (min)

A

B

Hint

Use the two vertices whose classes start at or above the threshold.

Stage 9 - Q3 - 4 marks

20249

Plot a scatter graph for the paired data. Describe the relationship.

x

1

2

3

4

5

6

7

8

y

24

30

34

38

39

45

48

Hint

Keep the two values from each column together.

Stage 9 - Q4 - 4 marks

20250

Draw a reasonable straight line of best fit. Give one approximate equation and explain why it fits.

y

0

1

2

3

4

5

6

7

8

9

10

0

20

40

60

80

100

x

Hint

Fit the overall pattern instead of joining successive points.

Stage 9 - Q5 - 5 marks

20251

Draw a back-to-back stem-and-leaf diagram for these times. Order leaves from each stem and include a key for each side.

Group A: time (s)

\(65,\ 62,\ 60,\ 59,\ 57,\ 56\)

\(54,\ 52,\ 50,\ 47,\ 47,\ 45\)

Group B: time (s)

\(46,\ 51,\ 55,\ 58,\ 60,\ 66\)

\(48,\ 53,\ 57,\ 60,\ 64,\ 68\)

Hint

Sort each group before putting its leaves beside the shared stems.

Stage 9 - Q6 - 4 marks

20252

The diagram records task-completion times. Find both medians and decide which group is typically faster by this measure.

Group A

Stem

Group B

4

7

9

8

5

2

4

6

8

9

0

3

5

7

9

6

1

2

4

7

0

2

6

8

7

0

\(\text{A key: }7\mid 4=47\text{ s}\)

\(\text{B key: }4\mid 8=48\text{ s}\)

Hint

For completion times, lower is faster.

Stage 9 - Q7 - 3 marks

20253

State the modal class and explain why the exact modal value is unknown.

Time (min)

Frequency

\(5\le t<10\)

3

\(10\le t<15\)

6

\(15\le t<20\)

10

\(20\le t<25\)

19

\(25\le t<30\)

7

Hint

Identify the largest count, not the largest class midpoint.

Stage 9 - Q8 - 5 marks

20254

Estimate the mean time to 1 decimal place. Show midpoint products and explain why the answer is an estimate.

Time (min)

Frequency

\(5\le t<10\)

8

\(10\le t<15\)

15

\(15\le t<20\)

13

\(20\le t<25\)

9

\(25\le t<30\)

6

Hint

Every class midpoint is repeated as many times as its frequency.

Stage 9 - Q9 - 4 marks

20255

These are transport categories for one survey. Choose a suitable diagram, sketch it, and explain why a frequency polygon is unsuitable.

Transport

Frequency

Walk

6

Cycle

7

Bus

13

Car

12

Hint

Decide whether the horizontal variable is categorical or numerical.

Stage 9 - Q10 - 8 marks

20256

A grouped table has classes \(0\le t<10\), \(10\le t<20\), \(20\le t<30\) and frequencies 3,6,3. Audit these claims: exact mean 15; median class 10–20; actual range 30. Support your answer with two raw datasets that match the table but have different means.

Hint

Distinguish an exact conclusion from an estimate and test it with compatible raw values.