smc-6531-10-Stem-and-Leaf

Statistics, STD1 2026 HSC 22

The stem-and-leaf plot shows the age of 24 volunteers at a charity event.

\(\begin{array}{c|l}
\text{Stem} & \quad \quad \text{Leaf} \\
\hline \rule{0pt}{2.5ex}1 & \ 3\ \ \ \ 5 \\
2 & \ 0\ \ \ \ 2\ \ \ \ 5 \\
3 & \ 0\ \ \ \ 2\ \ \ \ 4\ \ \ \ 6 \\
4 & \ 1\ \ \ \ 3\ \ \ \ 3\ \ \ \ 7\ \ \ \ 8\ \ \ \ 9 \\
5 & \ 0\ \ \ \ 2\ \ \ \ 2\ \ \ \ \textbf{X} \\
6 & \ 1\ \ \ \ 4\ \ \ \ 6\ \ \\
7 & \ 0\ \ \ \ 2\ \ \\
\end{array} \qquad \qquad \boxed{\begin{array}{l} \text{KEY:} \\ 3\,|\,2=32 \end{array}}\)

Describe the shape of the distribution. (1 mark)
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It is known that the upper quartile of the dataset is 55.
Find the value of \(\textbf{X}\). (2 marks)
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a. \(\text{Approximately symmetric}\)

b. \(\textbf{X}=8\)

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a. \(\text{Approximately symmetric}\)

b. \(\text{24 data values}\ \Rightarrow\ Q_3\ \text{is the average of the 18th and 19th values}\)

\(\text{18th value}=52, \ \ \text{19th value}=50+\textbf{X}\)

\(\dfrac{52+(50+\textbf{X})}{2}\)	\(=55\)
\(102+\textbf{X}\)	\(=110\)
\(\textbf{X}\)	\(=8\)

Statistics, STD2 S1 EQ-Bank 5 MC

The stem plot below shows the height, in centimetres, of 20 players in a junior football team.

A player with a height of 179 cm is considered an outlier because 179 cm is greater than

162 cm
169 cm
173 cm
175.5 cm

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`D`

Show Worked Solution

`Q_1 = (148 + 148)/2 = 148`

`Q_3 = (158 + 160)/2 = 159`

`IQR = 159-148 = 11`

`text{Upper fence}`	`= Q_3 + 1.5 xx IQR`
	`= 159 + 1.5 xx 11= 175.5`

`=> D`

Statistics, STD2 S1 2021 HSC 3 MC

The stem-and-leaf plot shows the number of goals scored by a team in each of ten netball games.

What is the mode of this dataset?

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`C`

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`\text{Mode} -> \text{data point with highest frequency}`

`\text{Mode} = 25`

`=> C`

Statistics, STD2 S1 2005 HSC 24a

Draw a stem-and-leaf plot for the following set of scores.
`21\ \ \ 45\ \ \ 29\ \ \ 27\ \ \ 19\ \ \ 35\ \ \ 23\ \ \ 58\ \ \ 34\ \ \ 27` (2 marks)

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What is the median of the set of scores? (1 mark)

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Comment on the skewness of the set of scores. (1 mark)

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b. `28`

c. `text(The data has a tail that stretches to the right)`

`:.\ text(Data is positively skewed.)`

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b. `text(10 scores)`

`:.\ text(Median)`	`= text{(5th + 6th)}/2`
	`= (27 + 29)/2= 28`

c. `text(The data has a tail that stretches to the right)`

`:.\ text(Data is positively skewed.)`

Statistics, STD2 S1 2006 HSC 4 MC

A set of scores is displayed in a stem-and-leaf plot.

What is the median of this set of scores?

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`C`

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`text(10 scores)`

`text(Median)= text{5th + 6th}/2= (28 + 38)/2= 33`

`=> C`

Statistics, STD2 S1 2008 HSC 3 MC

The stem-and-leaf plot represents the daily sales of soft drink from a vending machine.

If the range of sales is 43, what is the value of

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`A`

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`text(Range = High) – text(Low) = 43`

`:.\ 67 – text(Low)`	`= 43`
`text(Low)`	`= 24`

`:.\ N = 4`

`=> A`

Statistics, STD2 S1 2009 HSC 24a

The diagram below shows a stem-and-leaf plot for 22 scores.

What is the mode for this data? (1 mark)

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What is the median for this data? (1 mark)

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a. `78`

b. `46`

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a. `text(Mode) = 78`

b. `22\ text(scores)`

`=>\ text(Median is the average of 11th and 12th scores)`

`:.\ text(Median)= (45 + 47)/2=46`

Statistics, STD2 S1 2012 HSC 1 MC

A set of 15 scores is displayed in a stem-and-leaf plot.

What is the median of these scores?

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`D`

Show Worked Solution

`text(15 scores)\ \ =>\ \ text(Median is 8th)`

`:.\ \ text(Median is)\ \ 78`

`=> D`