3.04 Box plots

For each of the following sets of scores:

In competition, a diver must complete 8 rounds of dives. Her scores for the first 7 rounds are:

7.3, \, 7.4, \, 7.7, \, 8.4, \, 8.7, \, 8.9, \, 9.4

Determine her score in the 8th round if the upper quartile of all of her 8 scores is 8.85.

Below is the luggage weight of 30 passengers:

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

The finishing times (in minutes) of the competitors in a 1500 \text{ m} swimming race are listed below:

The following list shows the number of points scored by a basketball team in each game of their previous season:

An advertising agency recorded the number of viewers within various age ranges of its newest television advertisement when it went to air. The results are shown in the table:

To gain a place in the main race of a car rally, teams must compete in a qualifying round. The median time in the qualifying round determines the cut off time to make it through to the main race. Below are some results from the qualifying round:

• 75\% of teams finished in 159 minutes or less.

• 25\% of teams finished in 132 minutes or less.

• 25\% of teams finished between with a time between 132 and 142 minutes.

Consider the following ogive:

Consider the following ogive:

The airline Flo Air decided to keep track of flight delay times (the number of minutes after the scheduled time when the plane takes off) over a week. The 100 results are shown in the dot plot:

a

Find the median delay time of the flights, in minutes.

b

Find the upper quartile.

c

Find the lower quartile.

d

Find the interquartile range.

e

If a flight is delayed for 10 minutes or more, the airline incurs a fee. Find the percentage of flights over the week for which the airline incurred a fee.

f

A rival airline, Fly Air, had a mean delay time during the same week of 45 minutes. Find the percentage of Flo Air’s flights that had longer delay times than Fly Air’s mean delay time.

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 if necessary.

\text{VO}_2 \text{Max} is a measure of how efficiently your body uses oxygen during exercise. The more physically fit you are, the higher your \text{VO}_2 \text{Max}. Here are some people's results, listed in ascending order, when their \text{VO}_2 \text{Max} was measured:

21,\, 21,\, 23,\, 25,\, 26,\, 27,\, 28,\, 29,\, 29,\, 29,\, 30,\, 30,\, 32,\, 38,\, 38,\, 42,\, 43,\, 44,\, 48,\, 50,\, 76

Construct a box plot for each of the following histograms:

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f

Match the histograms on the left to the corresponding box plots on the right:

Histogram A

Histogram B

Histogram C

Box Plot 1

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Box Plot 2

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Box Plot 3

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Histogram D

Box Plot 4

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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:

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

A class took an English test and a Mathematics test. Both tests had a maximum possible mark of 20. The parallel box plots below shows the results of the tests:

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:

A survey is conducted on the price of concert tickets locally and the price of the same concert at an international venue. The results are given in the back-to-back stem plot below:

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

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:

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:

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 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 test scores of 11 students in Drama and German are listed below:

• Drama: 75,\, 85,\, 62,\, 65,\, 52,\, 76,\, 89,\, 83,\, 55,\, 91,\, 77

• German: 82,\, 86,\, 76,\, 84,\, 64,\, 73,\, 89,\, 62,\, 54,\, 69,\, 78

Draw a parallel box plots for this data.