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Stage 9 - Q1 - 3 marks
20207

Find the modal time in each group and explain how the repeated leaves identify it.

Group A
Stem
Group B
3
7
9
9
8
4
2
4
6
8
9
0
3
5
7
9
5
1
2
4
7
0
2
2
6
8
6
0
\(\text{A key: }7\mid 3=37\text{ s}\)
\(\text{B key: }3\mid 8=38\text{ s}\)
Hint

A leaf must be combined with its own stem.

Stage 9 - Q2 - 4 marks
20208

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
2
4
4
7
9
3
5
8
5
1
3
4
6
7
9
0
2
4
5
7
7
6
2
1
3
5
\(\text{A key: }2\mid 4=42\text{ s}\)
\(\text{B key: }4\mid 3=43\text{ s}\)
Hint

For completion times, lower is faster.

Stage 9 - Q3 - 4 marks
20209

Find both ranges. Which group has more consistent times when consistency is judged by range?

Group A
Stem
Group B
4
4
6
6
9
5
7
5
1
3
5
6
8
9
0
2
4
6
7
9
9
6
1
4
3
5
7
\(\text{A key: }4\mid 4=44\text{ s}\)
\(\text{B key: }4\mid 5=45\text{ s}\)
Hint

Read the smallest left-side leaf nearest its stem, not the farthest leaf.

Stage 9 - Q4 - 4 marks
20210

Find each mean completion time to 1 decimal place. Compare which group is faster on average by this measure.

Group A
Stem
Group B
3
3
5
5
8
4
6
9
4
0
2
4
5
7
8
1
3
5
6
8
8
5
0
3
2
4
6
\(\text{A key: }3\mid 3=33\text{ s}\)
\(\text{B key: }3\mid 4=34\text{ s}\)
Hint

The number of leaves gives the divisor.

Stage 9 - Q5 - 4 marks
20211

Now these are timing estimates: the target is exactly 56 s. Which group median is closer to the target? Explain why “smaller is better” is inappropriate here.

Group A
Stem
Group B
4
5
7
7
6
8
5
0
2
4
6
7
9
1
3
5
7
8
6
0
2
5
0
0
4
6
8
\(\text{A key: }5\mid 4=45\text{ s}\)
\(\text{B key: }4\mid 6=46\text{ s}\)
Hint

Accuracy is closeness to the target on either side.

Stage 9 - Q6 - 4 marks
20212

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
9
8
5
2
4
6
8
9
0
3
5
7
9
6
1
2
4
7
0
2
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 - 4 marks
20213

Find each mean completion time to 1 decimal place. Compare which group is faster on average by this measure.

Group A
Stem
Group B
2
3
5
5
8
4
6
9
3
0
2
4
5
7
8
1
3
5
6
8
8
4
0
3
2
4
6
\(\text{A key: }3\mid 2=23\text{ s}\)
\(\text{B key: }2\mid 4=24\text{ s}\)
Hint

The number of leaves gives the divisor.

Stage 9 - Q8 - 5 marks
20214

Add one valid new A observation of 94 s to the original diagram. Calculate the new range and median, and compare how much each changes.

Group A
Stem
Group B
2
5
7
7
6
8
3
0
2
4
6
7
9
1
3
5
7
8
4
0
2
5
0
0
4
6
8
\(\text{A key: }5\mid 2=25\text{ s}\)
\(\text{B key: }2\mid 6=26\text{ s}\)
Hint

Recalculate the middle position after the sample size changes.

Stage 9 - Q9 - 4 marks
20215

Now these are timing estimates: the target is exactly 54 s. Which group median is closer to the target? Explain why “smaller is better” is inappropriate here.

Group A
Stem
Group B
4
3
5
5
8
4
6
9
5
0
2
4
5
7
8
1
3
5
6
8
8
6
0
3
2
4
6
\(\text{A key: }3\mid 4=43\text{ s}\)
\(\text{B key: }4\mid 4=44\text{ s}\)
Hint

Accuracy is closeness to the target on either side.

Stage 9 - Q10 - 6 marks
20216

These are completion times in seconds. Test the claim: “The groups have the same mean and range, so their distributions and medians must be the same.” Compare all three statistics and explain what can be said about typical speed.

Group A
Stem
Group B
1
0
2
4
6
8
0
0
6
6
8
\(\text{A key: }0\mid 1=10\text{ s}\)
\(\text{B key: }1\mid 0=10\text{ s}\)
Hint

A small set of summary numbers does not preserve every original value.

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