PROBLEMS ON HORIZONTAL AND VERTICAL GRAPH

Example 1 :

50 randomly selected students were asked to name their favorite subject at school. The results of the survey are displayed in the graph. 

a) What sort of graph is being used?

b) Which was the most favored subject?

c) How many students chose Art as their favorite subject? 

d) What percentage of the students named Mathematics as their favorite subject?

e) What percentage of the students chose either History or English as their favorite subject?

Solution :

(a)  Subjects used in the graph are

English, Mathematics, Science, Language, History, Geography, Music, Art

(b)  By observing the graph, science is the favorite subject.

(c)  For 6 students, art is the favorite subject.

(d)  Number of students who chooses math as their favorite subject is  =  8

Total number of students  =  50

Percentage of students who chooses math as favorite

=  (8/50) x 100%

=  16%

(e)  Number of students who chooses history  =  5,

for English  =  4

Percentage  =  [(5+4)/50] x 100%

=  (9/50) x 100%

=  18%

Example 2 :

In an English middle school, 80 students were asked to name their favorite fruit. The following data was collected :

a) Construct a vertical column graph to illustrate this data.

b) For this group of students, which was the most favored fruit?

c) Can we make conclusions about the favorite fruit of all middle school students from this survey? Give a reason for your answer.

Solution :

(a)  

(b)  By observing the graph, most favorite fruit is banana.

(c)  No, this is only one school in a particular area.

Example 3 :

A randomly selected sample of adults was asked to name the evening television news service that they watched. The following results were obtained:

a) How many adults were surveyed?

b) Which news service is the most popular?

c) What percentage of those surveyed watched the most popular news service?

d) What percentage of those surveyed watched CNN?

e) Draw a horizontal bar chart to display the data.

Solution :

(a)  Number of adults surveyed  =  40+45+64+25+23+3

=  200

(b)  By observing the table, most popular news channel is NBC.

(c)  Percentage of people who watches NBC 

=  (64/200) x 100%

=  32%

(d)  Number of people who watches CNN  =  45

Percentage  =  (45/200) x 100%

=  22.5%

(e)  

Example 4 :

100 randomly selected students at an international school were asked to indicate the continent of origin of their father. The data collected has been organized into the following frequency table. 

a) Display this data using a segmented bar chart. 

b) What percentage of the sample had fathers who were born outside Europe?

Solution :

(a)  

Except Europe  =  4+9+3+25+11

=  52

(b)  

Percentage of father's who born outside Europe

=  (52/100) x 100%

=  52%

Example 5 :

During the 2008 season Emma was very successful at scoring goals for her field hockey team. In fact on one occasion she scored 7 goals in a match. Her goal scoring results are illustrated on the graph.

a) How many games did Emma play?

b) On how many occasions did she score 4 or more goals?

c) In what percentage of games did she score:

i) less than 2 goals ii) more than 4 goals?

Solution :

In 2 games, she got 0 goals, in 3 games she got 2 goals etc.

(a)  Number of games she played  =  2+3+8+5+3+1+1

=  23 games

(b)  She scores 4 or more goals 

=  4 goals + 5 goals + 6 goals + 7 goals

=  5+3+1+1

=  10

In 10 games she has scored 4 or more goals.

(c)  (i)  Number of games she scores less than 2 goals

=  2 + 3 

=  5 games

Percentage  =  (5/23) x 100%

=  21.7%

(ii)  Number of games she scores more than 4 goals 

=  2 games

Percentage  =  (2/23) x 100%

=  0.086 x 100%

=  8.69%

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