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Stage 9 - Q1 - 3 marks
20197

Use both keys to read the smallest time in A, the largest time in B, and the number of observations in A.

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 repeated leaf still represents another observation.

Stage 9 - Q2 - 5 marks
20198

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)
\(62,\ 59,\ 57,\ 56,\ 54,\ 53\)
\(51,\ 49,\ 47,\ 44,\ 44,\ 42\)
Group B: time (s)
\(43,\ 48,\ 52,\ 55,\ 57,\ 63\)
\(45,\ 50,\ 54,\ 57,\ 61,\ 65\)
Hint

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

Stage 9 - Q3 - 5 marks
20199

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)
\(14.5,\ 14.2,\ 14.0,\ 13.9,\ 13.7,\ 13.6\)
\(13.4,\ 13.2,\ 13.0,\ 12.7,\ 12.7,\ 12.5\)
Group B: time (s)
\(12.6,\ 13.1,\ 13.5,\ 13.8,\ 14.0,\ 14.6\)
\(12.8,\ 13.3,\ 13.7,\ 14.0,\ 14.4,\ 14.8\)
Hint

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

Stage 9 - Q4 - 3 marks
20200

An additional time of 41 s belongs to A. Insert it in the correct place and state the new sample size. Keep both keys.

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

Insert the new value; do not replace an old leaf.

Stage 9 - Q5 - 4 marks
20201

The left-hand leaves in this diagram are ordered incorrectly. Redraw that side correctly and explain how to read it.

Group A
Stem
Group B
2
9
7
4
4
2
3
5
8
3
9
7
6
4
3
1
0
2
4
5
7
7
4
2
1
3
5
\(\text{A key: }2\mid 2=22\text{ s}\)
\(\text{B key: }2\mid 3=23\text{ s}\)
Hint

Read outward from the shared stem on both sides.

Stage 9 - Q6 - 4 marks
20202

These times are recorded to the nearest 0.1 second. Add a complete key on each side of the diagram and interpret one leaf from each group.

Group A
Stem
Group B
14
7
9
9
8
15
2
4
6
8
9
0
3
5
7
9
16
1
2
4
7
0
2
2
6
8
17
0
Hint

A key needs a real numerical value and its unit.

Stage 9 - Q7 - 3 marks
20203

An additional time of 44 s belongs to A. Insert it in the correct place and state the new sample size. Keep both keys.

Group A
Stem
Group B
3
6
8
8
7
9
4
1
3
5
7
8
2
4
6
8
9
5
0
1
3
6
1
1
5
7
9
\(\text{A key: }6\mid 3=36\text{ s}\)
\(\text{B key: }3\mid 7=37\text{ s}\)
Hint

Insert the new value; do not replace an old leaf.

Stage 9 - Q8 - 5 marks
20204

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)
\(14.2,\ 13.9,\ 13.7,\ 13.6,\ 13.4,\ 13.3\)
\(13.1,\ 12.9,\ 12.7,\ 12.4,\ 12.4,\ 12.2\)
Group B: time (s)
\(12.3,\ 12.8,\ 13.2,\ 13.5,\ 13.7,\ 14.3\)
\(12.5,\ 13.0,\ 13.4,\ 13.7,\ 14.1,\ 14.5\)
Hint

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

Stage 9 - Q9 - 4 marks
20205

These times are recorded to the nearest 0.1 second. Add a complete key on each side of the diagram and interpret one leaf from each group.

Group A
Stem
Group B
12
7
9
9
8
13
2
4
6
8
9
0
3
5
7
9
14
1
2
4
7
0
2
2
6
8
15
0
Hint

A key needs a real numerical value and its unit.

Stage 9 - Q10 - 6 marks
20206

Here overlined symbols denote two-digit numbers, not products. Group A has median 27 s, and the sum of all ten times is 286 s. Find digits a and b, then draw a back-to-back stem-and-leaf diagram with both keys.

\[A:\ 21,24,\overline{2a},31,35\]
\[B:\ 22,25,29,\overline{3b},36\]
Hint

Use the median to determine A first, then use the combined total.

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