Stem and leaf diagrams

Probability and statistics

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The unordered results are $21, 12, 24, 15, 33, 18, 24, 15, 30, 24$. Draw an ordered stem-and-leaf diagram. Use the key $1\mid 2$ means $12$.

2 marks
From the ordered diagram, write the mode.

Ordered stem-and-leaf diagram of group A
1 2 5 5 8
2 1 4 4 4
3 0 3
Key: 1 | 2 means 12

2 marks
Find the median and the range of group A.

3 marks
How many values in group A are greater than $25$? How many are at least $24$?

3 marks
Group B has values $5, 8, 12, 14, 16, 18, 20, 21, 25, 29$. Find the median and range of group B, and compare the medians with group A.

4 marks
Find the mean of group A.

4 marks
A student reads the key as $2\mid 4$ means $2.4$ instead of $24$. What median and range would that student get for group A?

5 marks
Compare group A with group B using the medians and ranges. How many results in group A are at least the median of group B?

6 marks

Mark scheme

Answer. 1 | 2 5 5 8
2 | 1 4 4 4
3 | 0 3
- The stems are $1, 2$ and $3$.
- The leaves in each row are written in order.
Answer. $24$
- $24$ appears three times.
- The mode is $24$.
Answer. Median $22.5$, range $21$
- The $5$th and $6$th values are $21$ and $24$.
- Median $= 22.5$ and range $= 33 - 12 = 21$.
Answer. $2$ and $5$
- Only $30$ and $33$ are greater than $25$.
- The three $24$s, $30$ and $33$ make five values.
Answer. Group B median $17$, range $24$. Group A has the higher median.
- The middle two values of group B are $16$ and $18$.
- Median $= 17$ and range $= 24$.
- Group A median $22.5$ is higher, so group A typically scored more.
Answer. $21.6$
- The total is $216$.
- Mean $= \dfrac{216}{10} = 21.6$.
Answer. Median $2.25$ and range $2.1$
- Every value is divided by $10$.
- The median becomes $2.25$ and the range becomes $2.1$.
Answer. Group A has the higher median. Group B has the larger range. Seven results in group A are at least $17$.
- Medians: $22.5$ and $17$, so group A is typically higher.
- Ranges: $21$ and $24$, so group B is slightly more spread out.
- The group A values at least $17$ are $18, 21, 24, 24, 24, 30, 33$.
- That is $7$ results.