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Stage 9 - Q1 - 3 marks
20217

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

Time (min)
Frequency
\(5\le t<10\)
4
\(10\le t<15\)
10
\(15\le t<20\)
18
\(20\le t<25\)
8
\(25\le t<30\)
5
Hint

Identify the largest count, not the largest class midpoint.

Stage 9 - Q2 - 4 marks
20218

Find the median class. Show the central observation position or positions and the cumulative frequencies.

Time (min)
Frequency
\(0\le t<5\)
6
\(5\le t<10\)
9
\(10\le t<15\)
13
\(15\le t<20\)
22
\(20\le t<25\)
10
Hint

Use the observations ordered by value, not the middle row of the table.

Stage 9 - Q3 - 4 marks
20219

Find the modal and median classes. Are they the same in this dataset?

Time (min)
Frequency
\(0\le t<10\)
6
\(10\le t<20\)
13
\(20\le t<30\)
11
\(30\le t<40\)
7
\(40\le t<50\)
4
Hint

A tallest row and a halfway observation describe different features.

Stage 9 - Q4 - 4 marks
20220

There are 56 observations in total. Find the missing frequency, then state the median class.

Time (min)
Frequency
\(15\le t<25\)
14
\(25\le t<35\)
15
\(35\le t<45\)
?
\(45\le t<55\)
9
\(55\le t<65\)
6
Hint

Complete the table before finding the median position.

Stage 9 - Q5 - 4 marks
20221

A pupil claims the exact median is \(40\) minutes because it is the midpoint of the median class. Evaluate the claim.

Time (min)
Frequency
\(15\le t<25\)
5
\(25\le t<35\)
8
\(35\le t<45\)
16
\(45\le t<55\)
10
\(55\le t<65\)
6
Hint

Many different raw datasets produce the same grouped frequencies.

Stage 9 - Q6 - 3 marks
20222

Find the modal class or classes. Explain why choosing only the first largest frequency would lose information.

Time (min)
Frequency
\(10\le t<15\)
6
\(15\le t<20\)
22
\(20\le t<25\)
20
\(25\le t<30\)
22
\(30\le t<35\)
7
Hint

Check whether the largest frequency occurs more than once.

Stage 9 - Q7 - 4 marks
20223

There are 45 observations in total. Find the missing frequency, then state the median class.

Time (min)
Frequency
\(5\le t<10\)
3
\(10\le t<15\)
6
\(15\le t<20\)
?
\(20\le t<25\)
19
\(25\le t<30\)
7
Hint

Complete the table before finding the median position.

Stage 9 - Q8 - 4 marks
20224

Find the modal and median classes. Are they the same in this dataset?

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

A tallest row and a halfway observation describe different features.

Stage 9 - Q9 - 4 marks
20225

A pupil claims the exact median is \(15\) minutes because it is the midpoint of the median class. Evaluate the claim.

Time (min)
Frequency
\(0\le t<10\)
11
\(10\le t<20\)
12
\(20\le t<30\)
9
\(30\le t<40\)
6
\(40\le t<50\)
3
Hint

Many different raw datasets produce the same grouped frequencies.

Stage 9 - Q10 - 7 marks
20226

Ten times are grouped as \(0\le t<10\) with frequency 5 and \(10\le t<20\) with frequency 5. Can one median class be identified with certainty? Give two compatible raw datasets whose medians lie in different classes.

Hint

For an even total, check both central observations; do not automatically choose the class where cumulative frequency first reaches half.

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