7.05 Box plots

For each of the the following sets of data:

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:

92,\, 94,\, 100,\, 103,\, 103,\, 105,\, 105,\, 109,\, 110,\, 113,\, 114,\\ 114,\, 116,\, 118,\, 118,\, 119,\, 120,\, 125,\, 125,\, 126,\, 130

Below is the luggage weight of 30 passengers:

Consider the grouped data displayed in the following column graph:

a

Complete a frequency table for this data.

b

Use the class centres to estimate:

i

The range

ii

The interquartile range

c

Use technology to construct a boxplot for the above data, then write down the five number summary.

The histogram shows the heights of tomato plants in a greenhouse:

In a survey the mass (in grams) of 30 individual apples from an orchard were noted and recorded in the following list:

86,\quad 87,\quad 91,\quad 93,\quad 94,\quad 95,\quad 96,\quad 96,\quad 98,\quad99

100,\quad 101,\quad 102,\quad 103,\quad 103,\quad 104,\quad 104,\quad 105,\quad 106,\quad 106

106,\quad 107,\quad 107,\quad 107,\quad 108,\quad 108,\quad 109,\quad 109,\quad 109,\quad 109

Use technology to construct a boxplot for the above data, then write down the five number summary.

For each of the following sets of data:

c

	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

d

e

Score	Frequency
15	13
16	9
17	23
18	19
19	8
20	13

f

Construct a box plot for each five number summary:

Consider the following data set:

20,\, 36,\, 52,\, 56,\, 24,\, 16,\, 40,\, 4,\, 28

The box plot shows the age at which a group of people got their driving licences:

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:

a

Find the median thickness, to two decimal places.

b

Find the interquartile range.

c

Construct a box plot to represent the data.

d

What percentage of thicknesses were between 10.8 \text{ mm} and 11.2 \text{ mm} inclusive? Round your answer to two decimal places.

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

Salaries earned by employees at a software company is given in the histogram below:

Minimum temperatures are recorded on a sample of days throughout the year and is given in the histogram below:

a

Using the class centres and technology construct a box plot.

b

Using the class centres find an estimate for the range.

c

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 below show the monthly profits (in thousands of dollars) of two derivatives traders over a year:

The parallel box plots shows the distances, in centimetres, jumped by two high jumpers:

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:

The parallel box plots show the number of goals scored by two football players in each season:

The parallel box plots below shows the data collected by the manufacturers on the life-span of light bulbs, measured in thousands of hours:

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:

The box plots below represent the daily sales made by Carl and Angelina over the course of one month:

Two bookstores recorded the selling price of all their books. The results are presented in the parallel box plots:

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

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:

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:

The batting scores of two cricket teams, A and B, are recorded in the back-to-back stem plot below:

The back-to-back stem plot below shows the number of pieces of paper used over several days by two classes, A and B:

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

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

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

Eileen competed in the high beam gymnastics event at both the 2006 and 2010 Nationals. Her judges' scores in both years are presented in the parallel box plots:

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:

A class took an English test and a Mathematics test. Both tests had a maximum possible mark of 25. The results are illustrated below.

In which test did the class tend to score better marks? Explain your answer.

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 \left(\text{bpm}\right), recorded throughout the season are presented in the box plots below:

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: