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.
There is a test to measure the Emotional Quotient (EQ) of an individual. Here are the EQ results for 21 people listed in ascending order:
90,\, 90,\, 91,\, 92,\, 93,\, 94,\, 95,\, 95,\, 95,\, 97,\, 99,\, 100,\, 108,\, 114,\, 116,\, 116,\, 117,\, 118,\, 118,\, 122,\, 129
Determine the median EQ score.
Determine the Upper Quartile score.
Determine the Lower Quartile score. Round your answer to one decimal place.
Below is the luggage weight of 30 passengers:
What is the mean check in weight? Round your answer to two decimal places.
Find the:
Median
Lower Quartile
Upper Quartile
In which quartile does the mean lie?
| Weight | Frequency |
|---|---|
| 16 | 5 |
| 17 | 5 |
| 18 | 2 |
| 19 | 4 |
| 20 | 6 |
| 21 | 4 |
| 22 | 4 |
Consider the grouped data displayed in the following column graph:
Complete a frequency table for this data.
Use the class centres to estimate:
The range
The interquartile range
Use your CAS calculator to construct a boxplot for the above data, then write down the five number summary.
Consider the following data set:
4,\, 27,\, 16,\, 29,\, 27,\, 10,\, 21,\, 12,\, 23,\, 8,\, 3,\, 1,\, 23,\, 9,\, 22
Find the five number summary using a CAS calculator.
Calculate the interquartile range.
The histogram shows the heights of tomato plants in a greenhouse:
Complete the following frequency table for this data:
| \text{Height (cm)} | \text{Class centre} | \text{Frequency} |
|---|---|---|
| 95 \leq x \lt 100 | 97.5 | |
| 100 \leq x \lt 105 | 3 | |
| 105 \leq x \lt 110 | ||
| 110 \leq x \lt 115 | ||
| 115 \leq x \lt 120 | ||
| 120 \leq x \lt 125 | 122.5 | |
| 125 \leq x \lt 130 | 4 | |
| 130 \leq x \lt 135 |
Use the class centres to estimate:
The range
The interquartile range
Use your CAS calculator to construct a boxplot for the above data, then write down the five number summary.
In a survey the masses of 30 apples from an orchard were noted and recorded below to the nearest gram:
86,\,87,\,91,\,93,\,94,\,95,\,96,\,96,\,98,\,99,\, 100,\, 101,\,102,\,103,\,103,\,104,\\ \,104,\,105,\,106,\,106,\,106,\, 107,\,107,\,107,\,108,\,108,\,109,\,109,\,109,\,109
Find the following statistics:
The smallest value
The largest value
The range
The first quartile
The third quartile
The interquartile range
Complete the following frequency table:
| \text{Weight (g)} | \text{Class centre} | \text{Number of apples} |
|---|---|---|
| 85 \leq x \lt 90 | 87.5 | |
| 90 \leq x \lt 95 | 3 | |
| 95 \leq x \lt 100 | ||
| 100 \leq x \lt 105 | ||
| 105 \leq x \lt 110 |
Use the class centres to estimate:
The range
The interquartile range
How much less was the estimation for the interquartile range than the actual interquartile range?
Use your CAS calculator to construct a boxplot for the above data, then write down the five number summary.
Consider the following stem plot:
Find the five number summary using a CAS calculator.
Calculate the interquartile range.
| Leaf | |
|---|---|
| 7 | 0\ 2\ 3\ 7\ 8\ 9 |
| 8 | 1\ 5\ 6\ 9 |
| 9 | 0\ 1\ 2\ 2\ 6\ 6\ 6\ 6\ 7\ 8 |
Key: 7 \vert 0 = 70
Consider the following data set:
47.1,\, 42.3,\, 41.8,\, 47.8,\, 27.1,\, 36.2,\, 31.8,\, 24,\, 48.2,\, 45.1,\, 47.2,\, 45.3,\, 43,\, 43,\, 39,\, 34.4
Find the five number summary using a CAS calculator.
Calculate the interquartile range.
Consider the following frequency table:
Find the five number summary using a CAS calculator.
Calculate the interquartile range.
| Score | Frequency |
|---|---|
| 15 | 13 |
| 16 | 9 |
| 17 | 23 |
| 18 | 19 |
| 19 | 8 |
| 20 | 13 |
Consider the following histogram:
Find the five number summary using a CAS calculator.
Calculate the interquartile range.
Consider the following grouped frequency table:
| Class | Class centre | Frequency |
|---|---|---|
| 40\leq x < 45 | 42.5 | 3 |
| 45\leq x < 50 | 47.5 | 4 |
| 50\leq x < 55 | 52.5 | 7 |
| 55\leq x < 60 | 57.5 | 3 |
| 60\leq x < 65 | 62.5 | 3 |
| 65\leq x < 70 | 67.5 | 9 |
| 70\leq x < 75 | 72.5 | 4 |
| 75\leq x < 80 | 77.5 | 5 |
Find the five number summary using a CAS calculator.
Calculate the interquartile range.
Consider the following dot plot:
Find the five number summary using a CAS calculator.
Calculate the interquartile range.
For the box plot shown, find the following:
Lowest score
Highest score
Range
Median
Interquartile Range
Consider the box plot and statistics listed below:
Median = 47
Lower Quartile = 33
Upper Quartile = 61
Lowest score = 16
Highest score = 71
Which number should go in position 2 on the box plot?
Consider the box plot and statistics listed below:
Median = 36
Lower Quartile = 28
Upper Quartile = 42
Lowest score = 20
Highest score = 52
Which number should go in position 4 on the box plot?
Using the information in the table, create a box plot to represent this data set:
| Minimum | 5 |
|---|---|
| Lower Quartile | 25 |
| Median | 35 |
| Upper Quartile | 60 |
| Maximum | 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 set:
20, 36, 52, 56, 24, 16, 40, 4, 28
Find the five number summary.
Construct a box plot for the data.
The box plot on the right shows the age at which a group of people got their driving licences:
What is the oldest age at which someone got their licence?
What is the youngest age at which someone got their licence?
What percentage of people 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 least spread out?
The bottom 50\% of responders were within how many years of one another?
Consider the box plot shown:
State the percentage of scores that lie between each of the following values:
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 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, to two decimal places.
Find the interquartile range.
Construct a box plot to represent 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 if necessary.
According to the box plot, in which quartile are the results the most spread out?
Which statistics cannot be found from a box plot?
The marks in an end-of-year exam for a class of students is given below:
52,\, 95,\, 80,\, 56,\, 59,\, 80,\, 86,\, 77,\, 80,\, 81,\, 78,\, 64,\, 84,\, 66,\, 96,\, 90
Construct a box plot for the data.
Calculate the interquartile range.
What percentage of marks lie in the range 85 to 96?
Which values do the lowest 75\% of scores lie between?
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 for his data:
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. Is his conclusion correct? Explain your answer.
Salaries earned by employees at a software company is given in the histogram below:
Use your CAS calculator to construct a box plot, using the class centres.
Calculate the interquartile range.
Using the box plot, approximately what percentage of salaries lie in the range \$90\,000 to \$100\,000?
Using the box plot, what can be said about the highest 25\% of salaries? Would this conclusion be different from using the histogram? Explain your answer.
Minimum temperatures are recorded on a sample of days throughout the year and is given in the histogram below:
Using the class centres and technology construct a box plot.
Using the class centres find an estimate for the range.
Using the box plot, approximately what percentage of temperatures lie in the range 2.5 \degree \text{C} to 12.5 \degree \text{C}?
The box plots show the monthly profits (in thousands of dollars) of two derivatives traders over a year.
Who made a higher median monthly profit?
Whose profits had a higher interquartile range?
Whose profits had a higher range?
How much more did Ned make in his most profitable month than Tobias did in his most profitable month?
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?
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 show the number of goals scored by two football players in each season:
Who scored the most goals in a 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?
Two groups of people, athletes and non-athletes, had their resting heart rate measured. The results are displayed in the given pair of box plots.
What is the median heart rate of athletes?
What is the median heart rate of the non-athletes?
Using this measure, which group has the lower heart rates?
What is the interquartile range of the athletes' heart rates?
What is the interquartile range of the non-athletes' heart rates?
Using this measure, which group has more consistent heart rate measures?
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 to the right.
For class 9P, find:
The median
The lower quartile
The upper quartile
The range
The interquartile range
For class 9Q, find:
The median
The lower quartile
The upper quartile
The range
The interquartile range
Which class tended to score better marks? Explain your answer.
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.
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? Explain your answer.
The box plots below represent the daily sales made by Carl and Angelina over the course of one month:
What is the range in Angelina's sales?
What is 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?
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.
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.
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 number of vehicles sold by two companies each week from a dealership over three months was recorded in the back-to-back stem plot:
Find the five number summary for the weekly number of vehicles sold over these three months by company A.
Find the five number summary for the weekly number of vehicles sold over these three months by company B.
Draw parallel box plots for this data.
| Company A | Company B | |
|---|---|---|
| 5\ 0 | 0 | 3\ 9 |
| 8\ 7\ 4\ 1\ 1\ 0 | 1 | 0\ 2\ 2\ 2\ 3\ 7 |
| 9\ 2\ 1\ 0 | 2 | 0\ 1\ 1\ 7 |
| 9 | 3 | 1 |
Key: 2 \vert 1 \vert 0 = 12 \text{ and }10
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
Ten participants had their pulse measured in beats per minute before and after exercise with results shown in the back-to-back stem plot on the right.
Find the five number summary for the participants' pulse before exercise.
Find the five number summary for the participants' pulse after exercise.
Draw a parallel box plots for this data.
| Pulse before | Pulse after | |
|---|---|---|
| 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 8 \vert 0 = 82 \text{ and }80
The batting scores of two cricket teams, A and B, are recorded in the back-to-back stem plot below:
Find the five number summary for the batting scores of team A.
Find the five number summary for the batting scores of team B.
Draw parallel box plots for this data.
| Team A | Team B | |
|---|---|---|
| 9\ 5 | 3 | 2\ 3\ 6\ 6\ 8 |
| 8\ 8\ 5\ 5\ 4\ 1 | 4 | 2\ 9 |
| 9\ 5 | 5 | 0\ 8 |
| 6 | 2 |
Key: 2 \vert 3 \vert 0 = 32 \text{ and }30
The back-to-back stem plot shows the number of pieces of paper used over several days by two classes, A and B:
Find the five number summary for the number of pieces of paper used in class A.
Find the five number summary for the number of pieces of paper used in class B.
Draw parallel box plots for this data.
| Class A | Class B | |
|---|---|---|
| 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 1 \vert 0 = 12 \text{ and }10
The back-to-back stem plot shows the test scores of two classes, A and B.
Draw parallel box plots for this data.
| Class A | Class B | |
|---|---|---|
| 5\ 5\ 0 | 6 | 1\ 5\ 9 |
| 9\ 8\ 4\ 3\ 2 | 7 | 1\ 4\ 7 |
| 5\ 5 | 8 | 0\ 4\ 7\ 9 |
| 9 | 2\ 7 |
Key: 2 \vert 7 \vert 0 = 72 \text{ and }70
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 length of time people in group A could hold their breath for.
Find the five number summary for the length of time people in group B could hold their breath for.
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 Olympics. Her judges' scores in both years are presented in the parallel box plots.
What was the difference between the minimum scores she was awarded?
What was the difference between the maximum scores 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?
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 box plots below:
How much greater was her median pulse rate after the sprint than before 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?