The following list shows the number of points scored by a basketball team in each game of their previous season:
59,\, 67,\, 73,\, 82,\, 91,\, 58,\, 79,\, 88,\, 69,\, 84,\, 55,\, 80,\, 98,\, 64,\, 82State the maximum value.
State the minimum value.
Find the median value.
Find the lower quartile.
Find the upper quartile.
The finishing times (in minutes) of the competitors in a 1500 \text{ m} swimming race are listed below:
18.48,\, 16.15,\, 25.66,\, 23.21,\, 18.57,\, 22.62,\, 20.49,\, 18.16,\, 19.73,\, 18.47,\, 20.23State the maximum value.
State the minimum value.
Find the median value.
Find the lower quartile.
Find the upper quartile.
The marks in an end-of-year exam for a class of students are listed below:
58,\, 69,\, 79,\, 89,\, 91,\, 52,\, 72,\, 75,\, 79,\, 77,\, 94,\, 81,\, 86,\, 50State the maximum value.
State the minimum value.
Find the median value.
Find the lower quartile.
Find the upper quartile.
For the box plot shown below, find each of the following:
Lowest score
Highest score
Range
Median
Interquartile range
Construct a box plot for each five number summary:
Median = 47
Lower Quartile = 33
Upper Quartile = 61
Lowest score = 16
Highest score = 71
Median = 36
Lower Quartile = 28
Upper Quartile = 42
Lowest score = 20
Highest score = 52
Median = 35
Lower Quartile = 25
Upper Quartile = 60
Lowest score = 5
Highest score = 75
A geography teacher has marked a set of tests. She wants to represent the results in a box plot. She has already sorted her data and created the table shown:
Create a box plot to match the data in the table.
| Minimum | 8 |
|---|---|
| Lower Quartile | 10 |
| Median | 16 |
| Upper Quartile | 24 |
| Maximum | 28 |
Consider the following data:
20, \, 36, \, 52, \, 56, \, 24, \, 16, \, 40, \, 4, \, 28
Find the five number summary.
Construct a box plot for the data.
Consider the box plot shown below:
State what percentage of scores lie between each of the following:
7 and 15
1 and 7
19 and 9
7 and 19
1 and 15
In which quartile is the data the least spread out?
The box plot below shows the age at which a group of people passed their driving licence test:
State the oldest age at which someone got their licence.
State the youngest age at which someone got their licence.
What percentage of the group were aged from 18 to 22?
The middle 50\% of responders were within how many years of one another?
In which quartile are the ages the least spread out?
The bottom 50\% of responders were within how many years of one another?
In training, a fighter pilot measures the number of seconds he blacks out over a number of flights. He constructs the following box-and-whisker plot:
As long as the pilot is not unconscious for more than 7 seconds, he will be safe to fly.
The pilot concludes that he is safe to fly all the time. Explain why his conclusion is incorrect.
The glass windows for an airplane are cut to a certain thickness, but machine production means there is some variation. The thickness of each pane of glass produced is measured (in millimetres), and the dot plot shows the results:
Find the median thickness.
Find the interquartile range.
Draw a box plot that represents the data.
What percentage of thicknesses were between 10.8 \text{ mm} and 11.2 \text{ mm} inclusive? Round your answer to two decimal places.
According to the box plot, in which quartile are the results the most spread out?
State whether the following can be determined from the box plot:
The mode thickness
The frequency of each thickness
The median thickness
The spread of thicknesses
The parallel box plots shows the distances, in centimetres, jumped by two high jumpers:
Who had a higher median jump?
Who made the highest jump?
Who made the lowest jump?
Who is the most consistent?
The parallel box plots show the number of goals scored by two football players in each season:
Who has the higher median number of goals for the season?
How many more goals did Holly score in her best season compared to Sophie in her best season?
What is the difference between the median number of goals scored in a season by each player?
What is the difference between the interquartile range for both players?
The parallel box plots shows the prices, in dollars, of the items on the menu of an upmarket restaurant and the menu of a fast food restaurant:
Which restaurant has the higher median price for the items they sell?
What is the difference between the median prices of the items sold by each restaurant?
Which restaurant has a greater price range for the items on the their menu?
What is the price difference between the most expensive items sold by each restaurant?
What amount of the cheapest item at the fast food restaurant could be bought for the same price of the most expensive item at the upmarket restaurant?
The parallel box plots below shows the data collected by the manufacturers on the life-span of light bulbs, measured in thousands of hours:
Complete the following table. Write each answer in terms of hours.
| Manufacturer A | Manufacturer B | |
|---|---|---|
| Median | ||
| Lower Quartile | ||
| Upper Quartile | ||
| Range | ||
| Interquartile Range |
Hence, which manufacturer produces light bulbs with the best lifespan? Explain your answer.
A mathematics test is given to two classes. The marks out of 20 received by students in each class are represented in the box plots below:
Complete the following table:
| Class 9P | Class 9Q | |
|---|---|---|
| Median | ||
| Lower quartile | ||
| Upper quartile | ||
| Range | ||
| Interquartile range |
Which class tended to score better marks? Explain your answer.
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 higher interquartile range?
Which trader's profits had a higher range?
How much more did Ned make in his most profitable month than Tobias in his most profitable month?
The box plots below represent the daily sales made by Carl and Angelina over the course of one month:
Find the range in Angelina's sales.
Find the range in Carl's sales.
By how much did Carl's median sales exceed Angelina's?
Considering the middle 50\% of sales for both sales people, whose sales were more consistent?
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 (\text{bpm}), recorded throughout the season are presented in the box plots below:
How much greater was her median pulse rate after the sprint than before the sprint?
Are her pulse rate readings more consistent before or after the sprint? Explain your answer.
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.
The heights (in metres) of the boys and girls in a class of 30 students were recorded. The results are given below:
Boy's heights: \, 1.65, 1.66, 1.67, 1.68, 1.63, 1.62, 1.61, 1.60, 1.75, 1.76, 1.77, 1.78, 1.73, 1.72, 1.71
Girl's heights: \, 1.55, 1.56, 1.57, 1.58, 1.53, 1.52, 1.51, 1.50, 1.69, 1.70, 1.71, 1.72, 1.67, 1.66, 1.65
Find the five number summary for the heights of boys in the class.
Find the five number summary for the heights of girls in the class.
Draw a parallel box plots for this data.
The test scores of 12 students in English and Music are listed below:
English: \, 55,\, 57,\, 63,\, 69,\, 71,\, 74,\, 77,\, 81,\, 84,\, 88,\, 91,\, 98
Music: \, 55,\, 61,\, 66,\, 69,\, 72,\, 74,\, 76,\, 81,\, 84,\, 86,\, 89,\, 93
Find the five number summary for the test scores for English.
Find the five number summary for the test scores for Music.
Draw parallel box plots for this data.
The data below represents how long each person in two different groups could hold their breath for, measured to the nearest second:
Group A: \, 13,\, 17,\, 22,\, 28,\, 32,\, 34,\, 44,\, 49,\, 55,\, 56,\, 63,\, 64,\, 66,\, 51,\, 39
Group B: \, 13,\, 18,\, 23,\, 28,\, 32,\, 36,\, 42,\, 44,\, 53,\, 56,\, 64,\, 67,\, 13,\, 45,\, 47
Find the five number summary for the times of people in Group A.
Find the five number summary for the times of people in Group B.
Draw a parallel box plots for this data.
Two friends, Rhonda and Michael, have been growing sunflowers. They have each measured the heights of their sunflowers to the nearest centimetre. The data from these measurements is shown below:
Rhonda: \, 3,\, 7,\, 7,\, 11,\, 16,\, 21,\, 24,\, 27,\, 28,\, 31,\, 41,\, 46,\, 49
Michael: \, 13,\, 18,\, 19,\, 23,\, 28,\, 35,\, 39,\, 46
Find the five number summary for the heights of Rhonda's sunflowers.
Find the five number summary for the heights of Michael's sunflowers.
Draw parallel box plots for this data.
Eileen competed in the high beam gymnastics event at both the 2006 and 2010 Asian Games. Her judges' scores in both years are presented in the parallel box plots:
What was the difference between the minimum scores, rounded to the nearest 0.25, she was awarded?
What was the difference between the maximum scores, rounded to the nearest 0.25, she was awarded?
One particular judge at the 2010 games gave Eileen score of 8.3. In which quartile of her 2006 scores would this lie?
In which year did the judges score Eileen most consistently?
A builder can choose between two different types of brick that are coloured red or yellow. The parallel box plots below shows the results of tests on the strength of the bricks:
Using the box plot, explain why a builder might to prefer to use the red bricks.
Using the box plot, explain why a builder might to prefer to use yellow bricks.
A class took an English test and a Mathematics test. Both tests had a maximum possible mark of 20. The results are illustrated below:
Compare the results of the two classes.
A cinema is showing three films, labelled A, B and C. The ages of people watching each of the films are illustrated in the parallel box plots:
Which film do you think has an adults only rating, restricting it to viewers 18 years of age and older? Explain your answer.
Which film would you recommend for a group of 15 year olds to watch? Explain your answer.
Which film would you recommend to a family of two parents in their 40's and two teenagers? Explain your answer.