13.04 Stem-and-leaf and dot plots
A group of people were surveyed on the number of websites they visit on a daily basis. The results are displayed in the given dot plot:
Complete the frequency table based on the dot plot:
| Number of websites visited daily | Frequency |
|---|---|
| 0 | |
| 1 | |
| 2 | |
| 3 | |
| 4 | |
| 5 | |
| 6 |
The given dot plot shows the number of students in each section of the school band:
Which section has the least members?
Find the number of people in the band.
How many more people are there in the Strings section than in the Brass section?
Each judge on a cooking show gives contestants a rating between 1 and 5. The dot plot shows the scores given to the winning contestant:
How many judges gave the contestant a rating of 4?
How many judges gave the contestant a rating of 4 or more?
How many judges gave the contestant a rating of 2 or less?
The goals scored by a football team in a single season are represented in the dot plot:
State the modal number of goals scored.
Find the median number of goals scored.
A group of adults are asked: "How old were you when you passed your driving test?". The responses were:
22, \, 17, \, 17, \, 17, \, 19, \, 21, \, 17, \, 22, \, 21, \, 18, \, 18, \, 17, \, 18, \, 22, \, 18Plot the responses on a dot plot.
Find the following:
Range
Mode
Median
How many people passed their driving test on or after their 19th birthday?
In a study, a group of people were shown 30 names, and after one minute they were asked to list the names they could remember. The results are presented in the dot plot:
How many people took part in the study?
What is the highest number of names someone remembered?
What was the lowest number of names someone remembered?
Find the range of names remembered.
Aviation glass is manufactured to be 12\text{ mm} thick. If the glass is too thin (less than 11.5\text{ mm}) or too thick (more than 12.5\text{ mm}) the aircraft will fail its glass safety check.
A regional airport conducts a glass safety check of all aircraft landing on their runways over a one month period and displays the results in the dot plot below:
How many aircraft were checked for glass safety?
State the lowest level of glass thickness measured.
State the modal glass thickness measured.
How many aircraft failed the glass safety check?
A supermarket manager takes a note every time an employee is late to work, and how late they were (rounded to the nearest half hour). The dot plot below shows their results for the last month:
Find the median amount of hours that employees were late by.
What fraction of late employees were later than the median amount?
If an employee is more than 1 hour late, the manager fines them \$10. How much money did the manager collect in fines over the last month?
The following dot plots display how many seconds it took for students to race from their classroom to their locker:
State the slowest time recorded.
Which teacher's class had the largest range of times?
Which teacher's class had the fastest student?
Which teacher's class had the slowest median time?
In each game of the season, a basketball team recorded the number of 'three-point shots' they scored. The results for the season are represented in the following dot plot:
How many games did they play during the season?
If the team scored 4 three-point shots in a game, how many points are scored from three-point shots?
What was the total number of points they scored from three-point shots during the season?
Hence find the mean number of points they scored per game from the three-point shots, correct to two decimal places.
This stem-and-leaf plot records the ages of customers at a beachside cafe last Sunday. Use the stem-and-leaf plot to complete the following frequency table:
| Leaf | |
|---|---|
| 1 | 1\ 5\ 9 |
| 2 | 2\ 3\ 5\ 6\ 7\ 9 |
| 3 | 0\ 1\ 2\ 4\ 6\ 7 |
| 4 | 1\ 3\ 4\ 6\ 8\ 9 |
| 5 | 1\ 4\ 7 |
| 6 | 2\ 4\ 5\ 6\ 7 |
Key: 5\vert 2 = 52
| Age | Frequency |
|---|---|
| 10-19 | |
| 20-29 | |
| 30-39 | |
| 40-49 | |
| 50-59 | |
| 60-69 |
An online booking service allows customers to book tickets to see performers in concert. Over the last month the service has been tracking how many tickets are sold in the first five seconds after they become available, and their results are displayed in the given stem-and-leaf plot:
How many concert events does this data set represent?
Find the highest number of tickets sold in the first five seconds.
Find the difference between the highest and lowest number of tickets sold in the first five seconds.
| Leaf | |
|---|---|
| 1 | 0\ 0\ 1\ 2\ 2\ 3\ 4\ 8 |
| 2 | 0\ 1\ 5\ 7\ 8\ 9 |
| 3 | 0\ 2\ 6\ 8 |
| 4 | |
| 5 | 6 |
Key: 1\vert 2 = 12 tickets sold
The following stem and leaf plot shows the age of people who enter through the gates of a theme park in the first ten minutes:
How many people passed through the gates in the first ten minutes?
State the age of the youngest person.
State the age of the oldest person.
Find the age difference between the youngest and oldest person.
| Leaf | |
|---|---|
| 1 | 1\ 2\ 3\ 3\ 4\ 4\ 6\ 6\ 7 |
| 2 | 0\ 2\ 4\ 9\ 9 |
| 3 | 2\ 5\ 5\ 5 |
| 4 | |
| 5 | 3 |
Key: 1\vert 2 = 12 years old
A city council selected a number of houses at random. They determined the fastest travel time (in minutes) from each house to the nearest hospital, and recorded the following results:25, \, 37, \, 16, \, 27, \, 27, \, 35, \, 21, \, 18, \, 19, \, 49, \, 14, \, 19, \, 31, \, 42, \, 18
Represent this data as an ordered stem-and-leaf plot.
Consider the given stem-and-leaf plot:
Find the mean of this data set.
| Leaf | |
|---|---|
| 1 | 2\ 6\ 8\ 9 |
| 2 | 0\ 2\ 9 |
| 3 | 0\ 2 |
Key: 1\vert 2 = 12
Consider the given stem-and-leaf plot:
Find the median of this data set.
| Leaf | |
|---|---|
| 1 | 2\ 9 |
| 2 | 4\ 6\ 7 |
| 3 | 0\ 4\ 5\ 6 |
| 4 | 3\ 5\ 7\ 9 |
| 5 | 0\ 2 |
| 6 | 5 |
| 7 | 3\ 9 |
| 8 | 4\ 5 |
Key: 5\vert 2 = 52
The level of mercury in 40 different water samples was tested and recorded in the following stem-and-leaf plot:
State the highest reading.
Find the 8th lowest reading.
How many readings of 100 or higher were recorded?
The level of mercury is deemed to be safe if the reading is 103 or lower. What fraction of the readings are safe?
| Leaf | |
|---|---|
| 9 | 3\ 3\ 3\ 3\ 6\ 7\ 8\ 8\ 9\ 9 |
| 10 | 0\ 0\ 3\ 3\ 4\ 4\ 5\ 5\ 6\ 7\ 9 |
| 11 | 2\ 3\ 4\ 4\ 5\ 6\ 8\ 9\ 9 |
| 12 | 0\ 1\ 1\ 1\ 2\ 2\ 3\ 5\ 6\ 7 |
Key: 1\vert 2 = 12 units
Roxanne is using a precision telescope to measure the size of craters (in \text{km}) closest to Olympus Mons on the surface of Mars. She records her findings in the given stem-and-leaf plot:
Find the median crater size.
Find the range of crater sizes.
Roxanne finds that the sum of all the crater sizes is 661. Find the mean crater size, correct to two decimal places.
| Leaf | |
|---|---|
| 1 | 1\ 2\ 3\ 6\ 7\ 8\ 8 |
| 2 | 1\ 3\ 4\ 5\ 5\ 5 |
| 3 | 0\ 1\ 1\ 2\ 3\ 4\ 4\ 5\ 7\ 8\ 8 |
| 4 | 0 |
Key: 1\vert 2 = 12 \text{ km}
The given stem-and-leaf plot shows the ages of 20 employees in a company:
Find the number of employees in their 30s.
State the age of the oldest employee.
State the age of the youngest employee.
Find the median age of the employees.
Find the modal age.
| Leaf | |
|---|---|
| 2 | 0\ 1\ 1\ 2\ 8\ 8\ 9 |
| 3 | 0\ 2\ 4\ 8\ 8 |
| 4 | 1\ 1\ 1\ 2\ 5 |
| 5 | 3\ 4\ 8 |
Key: 1\vert 2 = 12 years old
A cyclist measured his heart rate immediately after finishing each event in which he competed. The results are recorded in the following stem and leaf plot:
Calculate the difference between his slowest and fastest heart rate.
Calculate the mean heat rate of the cyclist, to the nearest whole number.
Find the median heart rate.
Find the modal heart rate.
For each extra heartbeat per minute, it takes 7 seconds longer for him to recover. How much longer would it take to recover when he finishes with the fastest heart rate, compared to when he finishes with the slowest heart rate?
| Leaf | |
|---|---|
| 16 | 1\ 4\ 4\ 4\ 6\ 8\ 8 |
| 17 | 0\ 0\ 4\ 6\ 8 |
| 18 | 0\ 2\ 3\ 3 |
| 19 | 1\ 2\ 3\ 4\ 7\ 7\ 8 |
Key: 1\vert 2 = 12 beats per minute