The residents of two blocks of townhouses were asked the number of pets they own. The frequency of various responses are presented in the following dot plots:
Is the pet ownership a little lower or higher in Block A than Block B?
In Block A, how many pets do most households have?
In Block B, how many pets do most households have?
Describe the shape of the data for Block A.
Find the range of the number of pets in Block A.
Which block has more variability in the the number of pets?
Do either sets of scores have an outlier?
Consider the following graph:
Which city has the highest average daily sunshine hours?
Which city has the month with the least average sunshine hours?
Which city has the greatest variation in sunshine hours over the year?
Consider the following side-by-side column graphs which compare the perceived and actual number of immigrants for 9 countries:
Which country has the greatest difference between actual and perceived number of immigrants?
Which country has the smallest difference between actual and perceived number of immigrants?
Which data set (perceived or actual) has the biggest range?
Consider the column graph that shows the records of a stationery shop on the number of pens and notebooks sold in one week:
Find the number of pens sold on Tuesday.
Find the number of notebooks sold on Friday.
Find the percentage of pens sold on Thursday correct to two decimal places.
Find the total number of pens and notebooks sold during the week.
Find the average average number of pens and notebooks sold per day.
Which is the better selling product?
Consider the column graph that shows the number of blood donations per month in a given year:
Which state had the most donations?
Both states show a period with a lower number of donations due to cold and flu symptoms preventing donors being eligible. Which period is this?
Autumn months
Summer months
Spring months
Winter months
Which month had the highest monthly donations?
If the total donated over a year across all states is 763\,542 units and 2\% is used for trauma and road accidents, how many units of blood are required in a year for these incidents?
Consider the column graph that shows the distribution of blood types in Australia, Egypt and the world, as of 2019:
Which blood type is most common?
Which blood type is the rarest?
In which of the blood types does Australia have a significant proportion less than the general world population?
Consider the blood type distributions given below:
| O+ | A+ | B+ | AB | O- | A- | B- | AB- | |
|---|---|---|---|---|---|---|---|---|
| Australia | 40\% | 31\% | 8\% | 2\% | 9\% | 7\% | 2\% | 1\% |
| Egypt | 52\% | 24\% | 12.4\% | 3.8\% | 5\% | 2\% | 0.6\% | 0.2\% |
Find the highest percentage difference between the proportion of a particular blood type between Egypt and Australia.
If, at the time that this data was collected, Australia had a population of 24\,642\,693 and Egypt had a population of 95\,220\,838, find the difference in the number of people with the blood type in part (d). Round your answer to the nearest whole number.
Consider the back-to-back column graph below which compares the ages of male and female students in a primary school:
Which distribution is positively skewed?
Which distribution has the highest mean?
Consider the back-to-back column graph below which compares the unemployment rates of Texas and California over a 30-year period:
Which state had rates most strongly skewed in a positive direction?
Which state had the highest modal rate?
Which state has a more symmetrical distribution of unemployment rates?
Consider the back-to-back column graphs below which compare the grades scored by females and males on a mathematics examination:
Which gender had the biggest range in scores?
Which gender was bi-modal?
Which gender had more students?
Which gender had more symmetrical results?
Which gender was more strongly skewed positively?
Consider the back-to-back histograms which compares the heights of female and male standard poodles:
Which data set is bi-modal?
Which data set has the highest range?
Which data set has the highest mean?
Which set is more positively skewed?
Consider the two histograms below which show the grade distributions in two university courses:
Which distribution has a clear mode?
Which distribution would be described as “uniform”?
Which distribution has the highest range?
Compare the mean and median of Section 1.
Which distribution would have the highest standard deviation?
State the modal class for males.
State the modal class for females.
Which gender has the highest numbers over 80 years old?
Two Science classes, each with 20 students, were given a 10-question True/False test. The results for each class are shown below:
Do you think Class 1 studied for their test? Justify your answer.
Do you think Class 2 studied for their test? Justify your answer.
Which statistic is the same for each class?
The weight (in kilograms) of two groups, A and B, were recorded in a stem plot as shown:
Find the mean weight of Group A.
Find the mean weight of Group B.
Which group contains individuals that are generally heavier?
Calculate the population standard deviation for Group A correct to one decimal place.
Calculate the sample standard deviation for Group B correct to one decimal place.
Which group had more consistent weights?
| Group A | Group B | |
|---|---|---|
| 5 | 0\ 1\ 1\ 2\ 3 | |
| 7\ 6\ 5\ 3\ 0 | 6 | 0\ 0\ 2\ 3 |
| 2\ 2\ 2\ 1\ 0 | 7 | 0 |
Key: 1|8|3 = 81 \text{ and } 83
Ten participants had their pulse measured before and after exercise with results shown in the stem-and-leaf plot:
What is the mode pulse rate after exercise?
Find the range of pulse rates before exercise.
Find the range of pulse rates after exercise.
Find the mean pulse rate before exercise.
Find the mean pulse rate after exercise.
Hence, what can you conclude about exercise and pulse rate from the measures of centre and spread?
| Pulse Rate Before Exercise | Pulse Rate After Exercise | |
|---|---|---|
| 5\ 5\ 0 | 5 | |
| 9\ 9\ 7\ 4 | 6 | |
| 4\ 3 | 7 | |
| 0 | 8 | 4 |
| 9 | 5\ 7\ 8 | |
| 10 | 3 | |
| 11 | 3\ 5\ 5 | |
| 12 | 0\ 1 |
The following stem-and-leaf plot shows the length (in minutes) of a random sample of phone calls made by Elizabeth and Kathleen:
Who made a 13-minute phone call?
Is Elizabeth’s median higher than Kathleen’s median?
Is Elizabeth's mean greater than her median?
| Elizabeth | Kathleen | |
|---|---|---|
| 3 | 1 | 0\ 7 |
| 5\ 3\ 2\ 2\ 2\ 0 | 2 | 3\ 8\ 8 |
| 9 | 3 | 1\ 1 |
| 8\ 5 | 4 | 7 |
| 6\ 2 | 5 | 2\ 4\ 8 |
Key: 2 \vert 2 \vert 6 = 22 \text{ and } 26
The back-to-back stem-and-leaf plot shows the number of desserts ordered at Hotel A and Hotel B over several randomly chosen days:
Interpret the lowest score for Hotel A.
Which hotel's median is higher?
Is the mean greater than the median in both groups?
| Hotel A | Hotel B | |
|---|---|---|
| 3 | 0 | |
| 4\ 3\ 2 | 1 | 3\ 4 |
| 7\ 6 | 2 | 7 |
| 4\ 3 | 3 | 3\ 4 |
| 6 | 4 | 6\ 7 |
| 2 | 5 | 2\ 3\ 4 |
Key: 2 \vert 1 \vert 3 = 12 \text{ and }13
The back-to-back stem plot shows the total number of pieces of paper used over several days in two classes:
Determine whether the following statements are true or false:
Roald's students did not use 7 pieces of paper on any day.
James's median is higher than Roald’s median.
The median is greater than the mean in both groups.
| Roald's class | James's class | |
|---|---|---|
| 7 | 0 | 7 |
| 3 | 1 | 1\ 2\ 3 |
| 8 | 2 | 8 |
| 4\ 3 | 3 | 2\ 3\ 4 |
| 7\ 6\ 5 | 4 | 9 |
| 3\ 2 | 5 | 2 |
\text{Key: } 2 \vert 6 \vert 0 = 62 \text{ and }60
The stem-and-leaf plot shows the batting scores of two cricket teams, Team A and Team B:
Find the median score of Team A and the median for Team B.
Find the range of scores for Team A and the range for Team B.
Find the interquartile range for Team A and also for Team B.
Find the population standard deviation for Team A and also for Team B, to two decimal places.
Which team had more varied scores?
| Team A | Team B | |
|---|---|---|
| 7\ 6\ 2 | 6 | 2\ 6\ 8 |
| 8\ 6\ 5\ 2\ 2 | 7 | 1\ 5\ 7 |
| 8\ 4 | 8 | 1\ 4\ 7\ 9 |
| 9 | 4\ 7 |
Key: 6|1|2 = 12 \text{ and } 16
The Cancer Council surveyed 60 random people, asking them approximately how many hours they spent in the sun in the last month. The responders were split up into two groups, tourists and local residents and the results are shown below:
What is the median number of hours that each group spent in the sun?
If the two groups were combined, what would be the median number of hours spent in the sun?
If the two groups were combined, what would be the range of responses?
| Tourists | Locals | |
|---|---|---|
| 9\ 8\ 7\ 7\ 6\ 5\ 4\ 4\ 3\ 1\ 1 | 1 | 2\ 4\ 4\ 5\ 5\ 5\ 6\ 8\ 9 |
| 9\ 5\ 1\ 0 | 2 | 2\ 3\ 5\ 9 |
| 9\ 7\ 6\ 1 | 3 | 0\ 2\ 5 |
| 7\ 6\ 6\ 5\ 4\ 3\ 1 | 4 | 0\ 0\ 2\ 3\ 6\ 6\ 7\ 8 |
| 9\ 6\ 3\ 0 | 5 | 2\ 2\ 3\ 5\ 8\ 9 |
\text{Key: }6 \vert 1 \vert 2 = 12 \text{ and } 16
The stem-and-leaf plot shows the batting scores of two cricket teams, A and B:
What is the highest score in Team A?
What is the highest score in Team B?
Find the mean score of Team A.
| A | B | |
|---|---|---|
| 5\ 2 | 3 | 2\ 3\ 5\ 7\ 9 |
| 9\ 8\ 5\ 4\ 2\ 1 | 4 | 2\ 9 |
| 8\ 2 | 5 | 3\ 6 |
| 6 | 4 |
Key: 6 | 1 | 2 = 12 \text{ and } 16
The data below shows the results of a survey conducted on the price of concert tickets locally and the price of the same concerts at an international venue:
What was the most expensive ticket price at the international venue?
What was the median ticket price at the international venue?
What percentage of local ticket prices were cheaper than the international median?
At the international venue, what percentage of tickets cost between \$90 and \$110 (inclusive)?
At the local venue, what percentage of tickets cost between \$90 and \$100 (inclusive)?
| Local | International | |
|---|---|---|
| 7\ 5\ 2\ 2 | 6 | 0\ 5 |
| 9\ 6\ 5\ 4\ 0 | 7 | 2\ 3\ 8\ 8 |
| 9\ 6\ 5\ 3\ 0 | 8 | 2\ 3\ 7\ 8 |
| 8\ 7\ 4\ 3\ 1 | 9 | 0\ 1\ 6\ 7\ 9 |
| 5 | 10 | 0\ 2\ 3\ 5\ 8 |
Key: 6|1|2 = \$16 \text{ and }\$12
The stem-and-leaf plot shows the test scores of two Year 11 classes, A and B:
Find the highest score in Class A.
Find the highest score in Class B.
Find the mean score of Class A, to two decimal places.
Find the mean score of Class B, to two decimal places.
Calculate the overall mean of all of the Year 11 students, to two decimal places.
| Class A | Class B | |
|---|---|---|
| 8\ 3\ 0 | 6 | 2\ 4\ 6 |
| 9\ 7\ 6\ 3\ 1 | 7 | 3\ 5\ 8 |
| 8\ 2 | 8 | 1\ 3\ 6\ 8 |
| 9 | 2\ 5 |
Key: 6 | 1 | 2 = 12 \text{ and } 16
The data below shows the results of a survey conducted on the price of concert tickets locally and the price of the same concert at an international venue:
Find the five number summary for the price of concert tickets at local venues.
Find the five number summary for the price of concert tickets at international venues.
Draw parallel box plots for this data.
| Local | International | |
|---|---|---|
| 7\ 6\ 3\ 0 | 6 | 1\ 8 |
| 8\ 6\ 4\ 3\ 2 | 7 | 3\ 5\ 5\ 9 |
| 9\ 6\ 5\ 1\ 1 | 8 | 1\ 5\ 7\ 9 |
| 8\ 7\ 5\ 2\ 0 | 9 | 1\ 3\ 4\ 6\ 8 |
| 1 | 10 | 1\ 2\ 4\ 7\ 8 |
Key: 2 \vert 6 \vert 0 = 62 \text{ and }60
The data below represents how long each student in two different classes could hold their breath for, measured to the nearest second:
Mrs Nguyen's class: \, 55,\, 59,\, 61,\, 66,\, 71,\, 75,\, 80,\, 89,\, 91,\, 95,\, 101,\, 103,\, 103,\, 109,\, 111
Miss Humphreys's class: \, 51,\, 66,\, 67,\, 68,\, 77,\, 78,\, 79,\, 81,\, 83,\, 85,\, 85,\, 86,\, 92,\, 101,\, 110
Display the data in a back-to-back stem plot.
Who is the teacher of the student who can hold their breath the longest?
If you want to determine which class, in general, has the stronger breath hold capacity, which measure would be most appropriate to use?
If you want to determine which class, in general, has the more consistent breath hold capacity, which measure would be most appropriate to use?
Two friends have been growing sunflowers. They have measured the height of their sunflowers to the nearest centimetre, with their results shown below:
Tricia: \, 39,\, 18,\, 14,\, 44,\, 37,\, 18,\, 23,\, 28
Quentin: \, 49,\, 25,\, 42,\, 5,\, 47,\, 12,\, 15,\, 8,\, 35,\, 22,\, 28,\, 6,\, 21
Display the data in a back-to-back stem plot.
Find the median height of Tricia's sunflowers.
Find the median height of Quentin's sunflowers.
Find the mean height of Tricia's sunflowers.
Find the mean height of Quentin's sunflowers. Round your answer to two decimal places.
Which friend generally grows taller plants?