Exam-Style Problems

Stage 9 - Q1 - 3 marks

20157

The class \(30\le t<40\) has frequency 13. A pupil plots \((30,13)\) on a frequency polygon. Correct the plotted point and explain.

Hint

Average the two class boundaries.

Stage 9 - Q2 - 4 marks

20158

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

Time (min)

Frequency

\(15\le t<20\)

6

\(20\le t<25\)

7

\(25\le t<30\)

16

\(30\le t<35\)

8

\(35\le t<40\)

4

Hint

Find the middle of each interval before plotting.

Stage 9 - Q3 - 4 marks

20159

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

Score

Frequency

\(16\text{–}25\)

3

\(26\text{–}35\)

5

\(36\text{–}45\)

15

\(46\text{–}55\)

5

\(56\text{–}65\)

2

Hint

Find the middle of each interval before plotting.

Stage 9 - Q4 - 3 marks

20160

The polygon represents the five classes of width 5 minutes, starting at 20. State the frequency for \(35\le t<40\) and the total number of observations.

Frequency

20

25

30

35

40

45

0

5

10

15

Time (min)

Hint

The class centre locates the correct vertex.

Stage 9 - Q5 - 4 marks

20161

The table contains 27 observations. Find the missing frequency, then draw its frequency polygon.

Time (min)

Frequency

\(0\le t<10\)

2

\(10\le t<20\)

7

\(20\le t<30\)

12

\(30\le t<40\)

?

\(40\le t<50\)

1

Hint

The frequencies must add to the stated number of observations.

Stage 9 - Q6 - 3 marks

20162

The class \(15\le t<20\) has frequency 7. A pupil plots \((15,7)\) on a frequency polygon. Correct the plotted point and explain.

Hint

Average the two class boundaries.

Stage 9 - Q7 - 4 marks

20163

Merge each neighbouring pair of classes in the table. Give the three new frequencies and their midpoint coordinates for a new polygon.

Time (min)

Frequency

\(5\le t<15\)

6

\(15\le t<25\)

9

\(25\le t<35\)

13

\(35\le t<45\)

5

\(45\le t<55\)

4

\(55\le t<65\)

7

Hint

Merging keeps every observation; it does not average frequencies.

Stage 9 - Q8 - 4 marks

20164

The table contains 31 observations. Find the missing frequency, then draw its frequency polygon.

Time (min)

Frequency

\(10\le t<15\)

3

\(15\le t<20\)

8

\(20\le t<25\)

?

\(25\le t<30\)

7

\(30\le t<35\)

1

Hint

The frequencies must add to the stated number of observations.

Stage 9 - Q9 - 4 marks

20165

Merge each neighbouring pair of classes in the table. Give the three new frequencies and their midpoint coordinates for a new polygon.

Time (min)

Frequency

\(10\le t<20\)

5

\(20\le t<30\)

6

\(30\le t<40\)

15

\(40\le t<50\)

5

\(50\le t<60\)

3

\(60\le t<70\)

6

Hint

Merging keeps every observation; it does not average frequencies.

Stage 9 - Q10 - 6 marks

20166

Four equal-width classes have midpoints 5, 15, 25, 35 and frequencies 4, x, 9, y. There are 34 observations and x is twice y. Complete and draw the frequency polygon. Could the same ratio condition hold if the total were 35 instead?

Hint

Frequencies count observations, so they must be non-negative integers.