CAPITULO VI MARCO LEGAL
6.5 APOYOS TECNOLÓGICOS PARA LA EXPORTACIÓN PYMES
1 The back-to-back stem-and-leaf
plot shows the amount of cash (in dollars) carried by a sample of Year 11
students at Mavbalear Senior High.
Boys Girls a Find the mean amount of cash
(to the nearest cent) carried by each group.
b Find the median amount of cash carried by each group.
c Find the range and interquartile range of each group.
d For each group:
i describe the shape ii identify any outliers and clusters.
e Who generally carries more cash boys or girls? Justify your answer.
SeeExample 11
during a season.
7 6 5 4 3 2 1 0 1 2 3 4 5 6 7
Frequency
0 1 2 3 4 5 6
Goals scored
Vale United Scorpions
a How many games were played by each team?
b How many goals were scored by:
i Scorpions ii Vale United?
c Find the mean number of goals scored by each team.
d What is the range for each team?
e Describe the shape of each team’s results.
f Which team performed better? Give reasons.
3 The daily maximum temperatures for Sydney and Perth in February are shown below.
20 22 24 26 28 30 32 34 36 38 40 42
Temperature (°C) Sydney
20 22 24 26 28 30 32 34 36 38 40 42
Temperature (°C) Perth
a Find the mean, median and modal temperatures for each city.
b Find the range and interquartile range of temperatures for each city.
c Describe the distribution shape of the temperatures for each city and identify any outliers and clusters.
d Compare the temperatures in Sydney and Perth. Comment on measures of location (the mean, median and mode), and measures of spread (range and interquartile range).
4 The results for two quizzes taken by a Year 10 History class are shown below.
a How many students are in the Year 10 History class?
b Find the mean and mode for each quiz.
c Find the median for each quiz.
d For each quiz, find:
i the range ii the interquartile range.
e Describe the distribution for each quiz, identifying any clusters and outliers.
f Are there significant differences between the results of the two quizzes? Justify your answer.
5 A survey to determine the number of people per household was conducted in several shopping centres.
The results are shown in the frequency histogram and boxplot on the right.
0 1
a How many households had 3 or more people?
b Find the:
i mode ii median
iii range iv interquartile range.
c Describe the shape of the distribution.
d According to the boxplot, what percentage of households had 2 or more people?
e Clustering occurs at 1 to 3 people per household.
How is this shown on the:
i frequency histogram? ii boxplot?
f What information is better seen on:
i the frequency histogram? ii the boxplot?
SeeExample 12
watching TV during one week.
10 12 14 16 18 20 22 24 26 28
Hours spent watching TV per week
10 12 14 16 18 20 22 24 26 28
Hours spent watching TV per week a How many students watched TV for:
i fewer than 15 hours per week? ii more than 20 hours per week?
b Find the:
i mode ii range iii interquartile range c What is the shape of the distribution? How is this shown by:
i the dot plot? ii the boxplot?
d Which display of data, the dot plot or boxplot, can be used to find:
i the mode? ii the median?
iii the number of students who watched TV for 25 hours?
iv the interquartile range?
7 The speeds of cars were monitored along a main road in two different suburbs. The results are shown in the back-to-back stem-and-leaf plot and the parallel boxplots.
Sunbeam Valley Bentley’s Beach 8 5
9 8 8 7 4 3 3 3 2 0 6 0 0 1 2 3 5 5 7 8 9
9 9 6 5 5 4 4 3 3 2 2 1 1 0 0 0 7 0 0 2 2 3 3 5 5 5 6 6
2 0 0 8 0 2 3 4 5 5 5 8
9 0
50 60 70 80 90
Speed (km/h) Sunbeam Valley
Bentley’s Beach
a Find the range, median and interquartile range for each suburb.
b What is the shape of the distribution for each suburb?
c Are there any clusters or outliers in either suburb?
d According to the boxplot, what percentage of drivers in Bentley’s Beach drive faster than all drivers in Sunbeam Valley?
e In which suburb do drivers generally drive faster? Give a possible reason for your answer.
8 Lamissa and Anneka each shot arrows at a target 50 m away during an archery contest. They scored 10 for a bulls-eye down to 1 for the outer ring. Their results are displayed in the back-to-back histogram and the parallel box-and-whisker plots below.
1 2 3 4 5 6 7 8 9 10
a How many arrows each did Lamissa and Anneka shoot?
b Find the mode and median score per arrow for each contestant.
c Find the range and interquartile range for each contestant.
d Describe the shape of the distribution for each contestant.
e According to the boxplots, on what percentage of the arrows shot was a score of 6 or less achieved by:
i Lamissa? ii Anneka?
f Who was the better archer during this contest? Justify your answer by referring to the measures of location and spread.
9 The number of sit-ups per minute completed by men and women at the Full On Fitness Centre are displayed in the back-to-back histogram and parallel boxplots.
Women Men
Number of sit-ups per minute Men
10 20 30 40 50 60
Women
a Why would a dot plot be an inappropriate way to display the data shown above?
b What is the median number of sit-ups per minute completed by each group?
c Find the range and interquartile range for each group.
d Describe the shape of the distributions for women and for men.
e Which group has more spread in the number of sit-ups completed per minute? Give reasons for your answer.
Test results 10 Yellow
30 40 50 60 70 80 90
10 Blue 10 Red 10 Green
a What is the range of test results for:
i 10 Yellow? ii 10 Blue?
b For which class are the test results:
i positively skewed? ii negatively skewed? iii symmetrical?
c Which class had:
i the lowest interquartile range? ii the highest test score? iii the highest median?
d Which class had the best test results overall? Give reasons.