The stem plot 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:
Find the price of the most expensive ticket price at the international venue.
Calculate the median ticket price at the international venue.
Find the percentage of local ticket prices that were cheaper than the international median.
| 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: 2 \vert 6 \vert 0 = 62 \text{ and }60
At the international venue, find the percentage of tickets that cost between \$90 and \$110 (inclusive).
At the local venue, find the percentage of tickets that cost between \$90 and \$100 (inclusive).
The test scores of 12 students in Music and French are listed below:
Music: 79, 59, 74, 94, 51, 71, 93, 84, 69, 61, 86, 86
French: 62, 71, 64, 82, 83, 99, 87, 89, 66, 73, 59, 76
Display the data as an ordered back to back stem-and-leaf plot.
The back-to-back stem plot shows the total number of pieces of paper used over several days in two classes:
State the highest number of pieces of paper used on any one day.
Calculate the median number of pieces of paper for Charlie's students.
Calculate the mean for Maximillian's students. Round your answer to the nearest whole.
| Maximillian's students | Charlie's students | |
|---|---|---|
| 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 |
Key: 2 \vert 6 \vert 0 = 62 \text{ and }60
The stem and leaf plot displays the test scores of a school's two Year 7 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. Round your answer to two decimal places.
Find the mean score of class B. Round your answer to two decimal places.
| Class A scores | Class B scores | |
|---|---|---|
| 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: 2 \vert 6 \vert 0 = 62 \text{ and }60
Calculate the overall mean of the year 7 students, rounded to two decimal places.
10 participants had their pulse measured before and after exercise with results shown in the stem and leaf plot below:
| 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 |
Key: 2 \vert 6 \vert 0 = 62 \text{ and }60
Find the modal pulse rate after exercise.
Find the number of modes for the pulse rate before exercise.
Calculate the range of pulse rates before exercise.
Calculate the range of pulse rates after exercise.
Calculate the mean pulse rate before exercise.
Calculate the mean pulse rate after exercise.
Comment on the effect exercise seems to have on the mean and range of pulse rates.
The stem and leaf plot below shows the price of theatre tickets locally and internationally:
Calculate the five number summary of the price of concert tickets at local venues.
Calculate the five number summary of the price of concert tickets at international venues.
Hence draw a parallel box plot for this data.
| Local price | International price | |
|---|---|---|
| 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 stem and leaf plot shows the test scores of classes A and B:
Find the highest score in Class A.
Find the highest score in Class B.
Calculate the mean score of Class A. Round your answer to one decimal place.
Find the mean score of Class B. Round your answer to one decimal place.
Calculate the combined mean of the two classes correct to two decimal places.
| Class A | Class B | |
|---|---|---|
| 6\ 5\ 3 | 6 | 3\ 5 |
| 6\ 3\ 2\ 0 | 7 | 2\ 5\ 7\ 7 |
| 4\ 2\ 0 | 8 | 1\ 3\ 3\ 6 |
| 9 | 2\ 4 |
Key: 2 \vert 6 \vert 0 = 62 \text{ and }60
The weight (in kilograms) of a group of men and women were recorded and presented in the stem and leaf plot below:
Calculate the mean weight of the group of men. Round your answer to one decimal place.
Calculate the mean weight of the group of women. Round your answer to one decimal place.
Which group is heavier, on average?
| Weight of men | Weight of women | |
|---|---|---|
| 5 | 0\ 1\ 2\ 3\ 4\ 4\ 4\ 5\ 5\ 5\ 7 | |
| 9\ 8\ 8\ 7\ 6\ 6\ 6\ 5\ 3 | 6 | 0\ 2\ 2\ 3\ 4\ 7\ 7\ 8 |
| 6\ 4\ 3\ 2\ 2\ 1\ 0\ 0\ 0\ 0 | 7 | 0 |
| 0 | 8 |
Key: 2 \vert 6 \vert 0 = 62 \text{ and }60
The stem and leaf plot shows the number of books read in a year by a random sample of university and high school students:
Find the least number of books read by the university students.
Calculate the median number of books for the high school students.
Calculate the mean number of books for the university students. Round your answer to the nearest book.
| University students | High school students | |
|---|---|---|
| 7 | 0 | |
| 6\ 6\ 3 | 1 | 0\ 0\ 3\ 5 |
| 4\ 3\ 2\ 1 | 2 | 1\ 2\ 4\ 4\ 6 |
| 9\ 8\ 8\ 6 | 3 | 1\ 8\ 9 |
| 8\ 2 | 4 | 0\ 1 |
| 5 | ||
| 6 | ||
| 3 | 7 |
Key: 2 \vert 6 \vert 0 = 62 \text{ and }60
The back to back stem and leaf plot shows the length (in minutes) of a random sample of phone calls made by Sharon and Tricia:
Which girl made a 14 minute phone call?
State the length of the longest phone call.
Calculate the mean of Tricia's phone calls. Round your answer to the nearest minute.
Calculate the median of Sharon's phone calls. Round your answer to the nearest minute.
| Sharon's calls | Tricia's calls | |
|---|---|---|
| 3 | 1 | 3\ 4 |
| 7\ 6\ 4\ 3\ 2 | 2 | 6\ 7\ 8 |
| 9\ 8 | 3 | 2\ 4 |
| 4\ 3 | 4 | 1\ 2 |
| 7\ 6 | 5 | 6\ 7\ 8 |
Key: 2 \vert 6 \vert 0 = 62 \text{ and }60
The stem and leaf plot shows the number of desserts ordered at two hotels over several randomly chosen days of a month:
Which hotel had the largest range in number of desserts ordered?
Which hotel had the highest median number of desserts ordered?
| 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 6 \vert 0 = 62 \text{ and }60
The stem and leaf plot on the right shows the amount of cash (in dollars) carried by a random sample of teenage boys and girls.
Determine if the following statements are true or false:
The boys carried more cash than the girls.
The median value the boys carried was \$48.
The median amount carried by the girls was \$36.
Only the girls' distribution is roughly bell-shaped.
There was more variation among the girls.
There were no outliers in either group.
| Boy's cash | Girl's cash | |
|---|---|---|
| 7 | 0 | |
| 1 | 1 | 1 |
| 5\ 4\ 1 | 2 | 2\ 6\ 8 |
| 8\ 5\ 4 | 3 | 3\ 4\ 4\ 6\ 6\ 8\ 9 |
| 9\ 8\ 2\ 2\ 2\ 1 | 4 | 3\ 4\ 6 |
| 9\ 7\ 4\ 3 | 5 | 4 |
| 8\ 5\ 2 | 6 | |
| 3\ 1 | 7 |
Key: 2 \vert 6 \vert 0 = 62 \text{ and }60
For each of the stem and leaf plots below, which show the batting scores of two cricket teams, A and B:
Find the median score for Team A.
Find the median score for Team B.
Calculate the range of Team A’s scores.
Calculate the range of Team B’s scores.
Calculate the interquartile range of Team A’s scores.
Calculate the interquartile range of Team B’s 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: 2 \vert 6 \vert 0 = 62 \text{ and }60
| Team A | Team B | |
|---|---|---|
| 5\ 5 | 3 | 4\ 5\ 5\ 8\ 9 |
| 8\ 8\ 4\ 3\ 2\ 2 | 4 | 3\ 6 |
| 7\ 2 | 5 | 3\ 4 |
| 6 | 3 |
Key: 2 \vert 6 \vert 0 = 62 \text{ and }60
The box plots show the monthly profits (in thousands of dollars) of two derivatives traders over a year:
Which trader made a higher median monthly profit?
Which trader's profits had a greater interquartile range?
Which trader's profits had a greater range?
How much more did Ned make in his most profitable month than Tobias in his most profitable month?
The box plots show the distances, in centimetres, jumped by two high jumpers:
Which jumper had a higher median jump?
Which jumper made the highest jump?
Which jumper made the lowest jump?
Which jumper is the most consistent?
The heights (in metres) of the boys and girls in a class of 30 students were recorded. The results are given in the table below:
Find the five number summary of the heights of boys in the class.
Find the five number summary of the heights of girls in the class.
Hence draw a parallel box plot for this data.
| Boys | Girls |
|---|---|
| 1.65 | 1.55 |
| 1.66 | 1.56 |
| 1.67 | 1.57 |
| 1.68 | 1.58 |
| 1.63 | 1.53 |
| 1.62 | 1.52 |
| 1.61 | 1.51 |
| 1.60 | 1.50 |
| 1.75 | 1.69 |
| 1.76 | 1.70 |
| 1.77 | 1.71 |
| 1.78 | 1.72 |
| 1.73 | 1.67 |
| 1.72 | 1.66 |
| 1.71 | 1.65 |
The two box plots below show the data collected by the manufacturers on the life-span of light bulbs, measured in thousands of hours:
Copy and complete the following table for the two sets of data. Write each answer in terms of number of hours.
| Manufacturer A | Manufacturer B | |
|---|---|---|
| Median | ||
| Lower Quartile | ||
| Upper Quartile | ||
| Range | ||
| Interquartile Range |
Hence determine which manufacturer produces light bulbs with the longer lifespan?
A builder can choose between two different types of brick that are coloured red or yellow. The box plots below illustrate the results of tests on the strength of the bricks:
Explain why a builder may prefer to use red bricks.
Explain why a builder may prefer to use yellow bricks.
A class took an English test and a Mathematics test. Both tests had a maximum possible mark of 25. The results are illustrated below:
Copy and complete the following table using the two box plots:
| English | Mathematics | |
|---|---|---|
| Median | ||
| Lower Quartile | ||
| Upper Quartile | ||
| Range | ||
| Interquartile Range |
In which test did the class tend to score better marks?
The box plots below represent the daily sales made by Carl and Angelina over the course of one month:
Calculate the range for Angelina's sales.
Calculate the range for Carl’s sales.
By how much did Carl’s median sales exceed Angelina's?
Considering the middle 50\% of sales, which salesperson had the more consistent number of sales?
Which salesperson had a more successful sales month?
At every training session of the season, a cyclist measured her pulse rate before a sprint and after a sprint. The before and after rates, measured in beats per minute (bpm), recorded throughout the season are presented in the parallel box plots below:
By how much did her median pulse rate increase during the sprint?
Determine the interquartile range of her pulse rate before the sprint.
Determine the interquartile range of her pulse rate after the sprint.
Determine the range of her pulse rate before the sprint.
Determine the range of her pulse rate after the sprint.
Are her pulse rate readings more consistent before or after the sprint?
In the last session of the season, the cyclist recorded her highest pulse rate of the season both before and after the sprint. By how much did her pulse rate increase during this particular training session?
Two bookstores recorded the selling price of all their books. The results are presented in the parallel box plots:
Which bookstore had the more consistent prices?
Comparing the most expensive books in each store, how much more expensive is the one in store B?
True or False: 25\% of the books in Bookstore B are at least as expensive than the most expensive book in Bookstore A.
True or False: 25\% of the books in Bookstore B are cheaper than the cheapest book in Bookstore A.
Eileen competed in the high beam gymnastics event at both the 2006 and 2010 Olympics. The judges’ scores in both years are presented in the parallel box plots:
In which year did the judges score her higher overall?
In which year did the judges score Eileen most consistently?
The boxplots summarize results from a medical study. The treatment group received an experimental drug to relieve cold symptoms, and the control group received a placebo. The boxplots show the number of days each group continued to report symptoms:
Answer true or false to the following:
There is an outlier in the treatment group of 16.
The control group has the higher median number of days.
The skew is more prominent in the treatment group.
In the treatment group, cold symptoms lasted 0 to 12 days (range = 12) versus 4 to 12 days (range = 8) for the control group.
It appears that the drug had a positive effect on patient recovery.
The test scores of 11 students in Drama and German are listed below:
In which subject does there appear to be an outlier?
In which subject did the students perform better?
The following box-and-whisker plots display statistics on the points scored by two basketball teams in each of their matches last season:
State the median score for Team A.
State the median score for Team B.
Calculate the range for Team A’s scores.
Calculate the range of Team B’s scores.
Calculate the interquartile range of Team A’s scores.
Calculate the interquartile range of Team B’s scores.
Two weightlifters both record their number of repetitions with a 70 \text{ kg} bar over 30 days. The results are displayed in the box plots below:
Which weightlifter has the more consistent results?
Determine which of the following statistics supports your answer:
The mean.
The range.
The mode.
The graph is positively skewed.
Which statistic is the same for each weightlifter?
Which weightlifter can do the most repetitions of 70 \text{ kg}?
A class completed 40 questions for homework. The time needed for boys and girls to finish them was collected, and the data was presented as a parallel dot plot:
Which gender had the highest median time?
Which gender had the largest range?
Which group has the highest valued mode?
David and Eamon were taking part in a spelling bee. The dot plots show how many letters were in each word that each boy correctly spelt:
Who spelled more words correctly?
Who has the highest range?
Which boy's median word length was 7 letters?
Which boy is the best speller of long words?
20 people joined a group fitness class, and over two weeks, they were tested on the number of chin ups they can do.
The dot plots show the number of chin ups each person could do each week:
From the first to the second week, what was the increase in the median number of chin ups someone could do?
In week 1, the mean number of chin ups was 2.25. In week 2, did this average increase or decrease?
Mae and Amelia are goal shooters for their respective netball teams. The table shows the number of goals they scored in each game of the season.
Construct a dot plot for Mae's scores.
Construct a dot plot for Amelia's scores.
Calculate the median number of goals for Mae.
Which girl has the largest range of goals scored?
| Mae | Amelia | |
|---|---|---|
| \text{Game 1} | 2 | 1 |
| \text{Game 2} | 5 | 2 |
| \text{Game 3} | 4 | 2 |
| \text{Game 4} | 3 | 2 |
| \text{Game 5} | 4 | 3 |
| \text{Game 6} | 2 | 2 |
| \text{Game 7} | 2 | 3 |
| \text{Game 8} | 4 | 1 |
| \text{Game 9} | 3 | 3 |
The heart rates of the school football team and the school volleyball team were measured after running for five minutes on a treadmill:
| \text{Heart rate} | \text{No. of people} \\ \text{ in Volleyball team} | \text{No. of people} \\ \text{ in Football team} |
|---|---|---|
| 90 | 1 | 1 |
| 95 | 2 | 3 |
| 100 | 1 | 2 |
| 105 | 1 | 1 |
| 110 | 2 | 1 |
| 115 | 1 | 1 |
| 120 | 3 | 2 |
Construct a dot plot for the heart rates of the football team.
Construct a dot plot for the heart rates of the volleyball team.
How much greater is the median heart rate of the volleyball team than the football team?
Calculate the range of heart rates for the football team.
Which team appears to be the fittest overall? Explain your answer.
Three runners from an athletics team recorded their 100 metre race times over the past year:
Yuri: 13, 14, 13, 14, 16, 13, 15
Luigi: 13, 14, 13, 14, 15, 16, 14, 15, 15, 16
Ivan: 14, 15, 16, 16, 16, 13, 14, 16
Construct a dot plot for Yuri's times.
Construct a dot plot for Luigi's times.
Construct a dot plot for Ivan's times.
Which boy is the fastest runner over 100 metres?
By how much would Luigi's median time need to decrease to match Yuri's median time?
By how much would Ivan's median time need to decrease to match Yuri's median time?
Students from two different basketball teams at a school were asked how many times they eat takeaway food in a week. The results are displayed in the table below:
| Team A | 0 | 2 | 0 | 3 | 1 | 2 | 1 | 3 | 1 | 4 | 1 | 1 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Team B | 0 | 4 | 2 | 1 | 0 | 4 | 3 | 2 | 2 | 1 | 2 | 0 |
Construct a box plot for Team A.
Construct a box plot for Team B.
If the coach is only happy when students have an answer of 0 or 1, which team is the coach happiest with?
The residents of two blocks of townhouses were asked the number of pets they own. The frequency of various responses are presented in the dot plots.
In which block is pet ownership lower in general?
In which block do most households have zero or one pet?
In which block is there a greater range in the number of pets?
In which block is pet ownership skewed positively?
How many pets are there in total in block B?
A stationery shop kept a weekly record of the number of pens and notebooks sold:
Find the number of pens sold on Tuesday.
Find the number of notebooks sold on Friday.
Find the total number of notebooks sold during the week.
Find the total number of pens sold during the week
Find the percentage of pens sold on Thursday, rouding your answer to two decimal places.
Calculate the mean number of notebooks sold per day. Round your answer to one decimal place.
Calculate the mean number of pens sold per day. Round your answer to one decimal place.
Which is the better selling product? Justify your answer.
The following histograms show the season results of two soccer groups, Group A and Group B, and the number of games (frequency) in which they scored a certain number of goals (scores):
Calculate the modal number of goals for Group A.
Calculate the modal number of goals for Group B.
Calculate the range for Group A.
Calcuate the range for Group B.
Which group scored the lowest total number of goals during the season?
Which group had more varied results? Justify your answer.