smc-1128-24-Stem and Leaf

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?

Show Answers Only

`C`

Show Worked Solution

`\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)

--- 6 WORK AREA LINES (style=blank) ---
What is the median of the set of scores? (1 mark)

--- 2 WORK AREA LINES (style=lined) ---
Comment on the skewness of the set of scores. (1 mark)

--- 2 WORK AREA LINES (style=lined) ---

Show Answers Only

`28`
`text(The data has a tail that stretches to the right)`
`:.\ text(Data is positively Skewed.)`

Show Worked Solution

ii. `text(10 scores)`

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

iii. `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?

Show Answers Only

`C`

Show Worked Solution

`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

`4`
`5`
`24`
`25`

Show Answers Only

`A`

Show Worked Solution

`text(Range = High) – text(Low) = 43`

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

`:.\ N = 4`

`=> A`

Statistics, STD2 S1 2013 HSC 26f

Jason travels to work by car on all five days of his working week, leaving home at 7 am each day. He compares his travel times using roads without tolls and roads with tolls over a period of 12 working weeks.

He records his travel times (in minutes) in a back-to-back stem-and-leaf plot.

What is the modal travel time when he uses roads without tolls? (1 mark)

--- 1 WORK AREA LINES (style=lined) ---
What is the median travel time when he uses roads without tolls? (1 mark)

--- 1 WORK AREA LINES (style=lined) ---
Describe how the two data sets differ in terms of the spread and skewness of their distributions. (2 marks)

--- 5 WORK AREA LINES (style=lined) ---

Show Answers Only

`52\ text(minutes)`
`50.5\ text(minutes)`
`text(Spread)`
`text{Times without tolls have a tighter spread (range = 22)}`
`text{than times with tolls (range = 55).}`
`text(Skewness)`
`text(Times without tolls shows virtually no skewness while`
`text(times with tolls are positively skewed.)`

Show Worked Solution

i. `text(Modal time) = 52\ text(minutes)`

♦ Mean mark 36%
MARKER’S COMMENT: Finding a median proved challenging for many students. Take note!

ii. `text(30 times with no tolls)`

`text(Median)`	`=\ text(Average of 15th and 16th)`
	`=(50 + 51)/2`
	`= 50.5\ text(minutes)`

♦ Mean mark 39%

iii. `text(Spread)`

`text{Times without tolls have a much tighter}`

`text{spread (range = 22) than times with tolls}`

`text{(range = 55).}`

`text(Skewness)`

`text(Times without tolls shows virtually no skewness)`

`text(while times with tolls are positively skewed.)`

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)

--- 1 WORK AREA LINES (style=lined) ---
What is the median for this data? (1 mark)

--- 1 WORK AREA LINES (style=lined) ---

Show Answers Only

`78`
`46`

Show Worked Solution

i. `text(Mode) = 78`

ii. `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?

Show Answers Only

`D`

Show Worked Solution

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

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

`=> D`