7.05 Displaying and interpreting univariate data
State whether the following is true or false about an ordered stem-and-leaf plot:
The scores are ordered.
A stem-and-leaf plot does not give an idea of outliers and clusters.
It is only appropriate for data where scores have high frequencies.
The individual scores can be read on a stem-and-leaf plot.
This stem-and-leaf plot records the ages of customers at a beachside cafe last Sunday. Use the stem-and-leaf plot to construct a histogram for the data.
| 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:1 | 2 = 12
An online booking website allows customers to buy tickets to concerts. Over the last month, the website has been tracking how many tickets are sold in the first minute after they go on sale. The results are displayed in this stem-and-leaf plot:
How many concert does this data set represent?
Find the greatest number of tickets sold for a concert in the first minute.
Find the difference between the greatest and least number of tickets sold in the first minute.
| 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 stem-and-leaf plot below shows the age of people to enter through the gates of a concert in the first 5 seconds.
Find the number of people who passed through the gates in the first 5 seconds.
Calculate the range of ages represented in the plot.
Find the mean and median age.
Find the proportion of concert-goers who were under 20 years old.
| Leaf | |
|---|---|
| 1 | 1\ 2\ 4\ 5\ 6\ 6\ 7\ 9\ 9 |
| 2 | 2\ 3\ 5\ 5\ 7 |
| 3 | 1\ 3\ 8\ 9 |
| 4 | |
| 5 | 8 |
Key:1 | 2 = 12 years old
A group of people were surveyed on the number of websites they visit on a daily basis, and the results are displayed in the given line plot:
Construct a frequency table for this data.
64 people are surveyed to find their shoe sizes, and the results are shown in the table.
| Shoe Size | 9 | 9\dfrac{1}{2} | 10 | 10\dfrac{1}{2} | 11 | 11\dfrac{1}{2} | 12 |
|---|---|---|---|---|---|---|---|
| Number | 3 | 8 | 6 | 4 | 1 | 7 | 7 |
Construct a line plot for this information.
Sophia is a casual nurse. She used a line plot to keep track of the number of shifts she did each week for a number of weeks.
In this line plot, what does each dot represent?
What was the most frequently occurring number of shifts per week?
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?
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 line plot.
Find the number of aircrafts that failed their glass safety check. Explain.
John had 7 blue marbles, 4 black marbles, 8 yellow marbles, 13 white marbles, and 6 red marbles. Construct a bar graph for this information.
Miss Yen recorded her students' favorite pets in the column graph below:
Which type of pet is most popular?
Which pet is least popular?
How many students picked a Fish as their favorite pet?
How many students were surveyed in total?
Mr. Price recorded his students' favorite book genre in the bar graph shown.
Which book genre is most popular?
Which book genre is least popular?
How many more students prefer Detective books than Drama books?
The CDC surveyed some random people, asking them to estimate approximately how much time they spent in the sun during the previous summer. The frequency histogram shows their responses.
Find the number of people who were surveyed.
Find the proportion of responders who spent at least 60 hours in the sun.
The sector graph given represents the market share of four brands:
Given that Brand C is twice as popular as Brand A, find the angle at the center for Brand D.
The sector graph shows the results of testing a new medication on 1080 patients:
Find the number of patients that showed improvement after using the medication.
Find the number of patients that showed some change after using the medication.
Find the percentage of patients that deteriorated after using the medication.
The sector graph given represents the number of people taking leave from work at a particular company:
If 25 people took leave in January, how many degrees represents 1 person?
Find the number of people who took leave in November.
Find the number of people who took leave between the beginning of November and the end of March.
Find the percentage who took leave in December. Round your answer to two decimal places.
The following circle graphs show the distribution of nuclear weapons owned by countries around the world:
Which country has the most nuclear weapons according to the circle graphs?
Which two countries have around half of the nuclear weapons that are not owned by Russia or the USA?
How many countries have more than 100 nuclear weapons?
Mr. Rodriguez recorded the number of pets of his students. He found that 15 students had no pets, 19 students had only one pet, 3 students had two pets and 8 students had three pets.
Decide the best type of display for the data and justify your choice.
Bob asked his students to choose their favorite toy. 35\% students picked cars, 10\% of the students picked planes, 30\% picked balls and 25\% picked video games.
Decide the best type of display for the data and justify your choice.
Construct the display chosen in part (a).
Consider the data in the frequency table.
Decide the best type of display for the data in the frequency table and justify your choice.
Construct the display chosen in part (a).
| Score | Frequency |
|---|---|
| 11 | 12 |
| 12 | 9 |
| 13 | 10 |
| 14 | 9 |
| 15 | 6 |
The average temperature for each month in Tallsville was recorded in the following table:
Which month was the hottest?
Which month was the coldest?
Which two months had the same average temperature?
| Month | Temperature |
|---|---|
| \text{January} | 32 |
| \text{February} | 24 |
| \text{March} | 29 |
| \text{April} | 21 |
| \text{May} | 27 |
| \text{June} | 31 |
| \text{July} | 25 |
| \text{August} | 19 |
| \text{September} | 15 |
| \text{October} | 29 |
| \text{November} | 26 |
| \text{December} | 30 |
The following frequency table shows the data distribution for the length of leaves collected from a species of tree in the botanical gardens:
How many leaves less than 60 \text{ mm} were collected?
What was the most common interval of leaf length collected?
Are leaves more likely to be at least 60 \text{ mm} in length?
Can we conclude from the table that there were no leaves collected with a length less than 5 \text{ mm}. Explain your answer.
| Leaf length, (mm) | Frequency |
|---|---|
| 0 \leq x \lt 20 | 5 |
| 20\leq x \lt 40 | 11 |
| 40\leq x \lt 60 | 19 |
| 60\leq x \lt 80 | 49 |
| 80\leq x \lt 84 | 43 |
As part of a fuel watch initiative, the price of gas at a service station was recorded each day for 21 days. The frequency table shows the results:
| Price (cents per liter) | Class Center | Frequency |
|---|---|---|
| 130.9 - 135.9 | 133.4 | 6 |
| 135.9 - 140.9 | 138.4 | 5 |
| 140.9 - 145.9 | 143.4 | 5 |
| 145.9 - 150.9 | 148.4 | 5 |
What was the greatest price that could have been recorded?
How many days was the price above 140.9 cents?
As part of a fuel watch initiative, the price of gas at a service station was recorded each day for 20 days. The frequency table shows the findings:
What was the greatest price that could have been recorded?
What is the modal price range?
What percentage of instances was the gas price in the modal price range?
If the class centers are taken to be the score in each class interval, find the total of the prices recorded.
Find the average fuel price.
| Price (in cents per liter) | Frequency |
|---|---|
| 130.0-134.9 | 5 |
| 135.0-139.9 | 6 |
| 140.0-144.9 | 3 |
| 145.0-149.9 | 4 |
| 150.0-154.9 | 2 |