Line and Bar Graphs

Line and Bar Graphs exercise

• Explain how to draw a bar graph.

  Hints

  Using a bar graph, you can see the relation between different data points much easier.

  Pay attention to the labelling of the axis: you observe the swimming pigs each day, not the day for each swimming pig.

  Here you see an example of a bar graph. It represents the number of burps of the different animals, including one human.

  Solution

  Here you see the given data on the left and the bar graph on the right.

  How can Frank draw such a bar graph?

  First, he needs to draw a coordinate plane. In this example the $x$-axis, or horizontal axis, is labeled by the day, and the $y$-axis, or vertical axis, is labeled by the number of swimming pigs.

  For each day, Frank draws a rectangle as high as the number of swimming pigs observed.

• Draw a line graph.

  Hints

  The day $3$ and day $4$ moods are the same.

  Highlight each line connecting nearby points.

  Solution

  Here you see the resulting line graph.

  First, we draw all the points corresponding to the data. From left to the right:

  • on day $1$, mood level $2$,
  • on day $2$, mood level $5$,
  • etc.

  Next, we connect nearby points with lines to get the line graph.

• Find the right data set for the bar graph.

  Hints

  Check each given data point.

  Let's recall how to draw a point in a coordinate system:

  • Draw a line parallel to the $y$-axis representing the day.
  • Draw a line parallel to the $x$-axis representing the number of carrots.
  • A point is given as the intersection of those two lines.

  For example, one data point is given by $(2,1)$, meaning that the pigs only ate one carrot on the second day.

  Solution

  Let's check all the given points:

  • The first day the pigs ate $3$ carrots.
  • The second day they ate just one.
  • On the third day they seem to be a little bit more hungry... they ate $5$ carrots.
  • The next day they ate $3$ carrots again.
  • From the fifth day one, they ate one carrot more than the day before: $4$ carrots on the fifth, $5$ carrots on the sixth, and $6$ carrots on the seventh day.

  Together we get the following data set:

  $\begin{array}{c|c|c|c|c|c|c|c} \text{day}&1&2&3&4&5&6&7\\ \hline \text{# of carrots}&3&1&5&3&4&5&6 \end{array}$

• Decide which graphs represent the data given.

  Hints

  If you replace each bar with a point and connect the resulting points, you get a line graph.

  There is one correct bar graph and one correct line graph for the given data.

  The $x$-axis is labelled with the first letter of the first names of Dorothy's friends, while the $y$-axis is labelled with the number of siblings.

  Solution

  Here you see both the bar as well as the line graph.

  • "Anne has $2$ siblings" is represented by the left-most bar.
  • "Bella just has $1$ sibling" is represented by the lowest bar, the second one from the left.
  • "Clara has $2$ siblings too" is represented by the third bar from the left.
  • The bar most right represents "Doris has $3$ siblings".

  If we replace each bar with a point and connect those points we get the corresponding line graph.

• Explain what line graphs and bar graphs are.

  Hints

  With line graphs one can recognize a trend much easier.

  Here you see an example of a line graph.

  This is the bar graph corresponding to the line graph above.

  Solution

  For both, bar graphs as well as line graphs, we draw a coordinate plane:

  • The $x$-axis is labeled with the days.
  • The $y$-axis is labeled with the number of observed pigs.

  For bar graphs, each data point is given by one bar, so the highs and lows can be seen easily.

  Line graphs also give the same information. Each bar is replaced with a point and the resulting points can be connected.

  As the number of data points grows greater and greater, bar graphs do not represent the data as well as line graphs.

• Interpret the different graphs.

  Hints

  To get the number corresponding to a name, just draw a line parallel to the $x$-axis passing through the corresponding point.

  The $y$-axis is always labelled with numbers.

  If the line graph contains a line parallel to the $x$-axis, then the numbers corresponding to the endpoints of the line are the same.

  Solution

  The number of breakfasts per week:

  • Anne eats breakfast only $1$ time.
  • Belle eats breakfast $5$ times.
  • Clare eats breakfast $4$ times.
  • Doris also eats breakfast $4$ times.

  The number of mobile phones owned:

  • Anne has $2$ mobile phones.
  • Belle and Clara just have $1$ mobile phone.
  • Doris has $3$ mobile phones at her disposal.

  The number of sneakers:

  • Anne has the least number of sneakers, namely $3$.
  • Bella has $4$ sneakers.
  • The other two Clara and Doris both have $5$ sneakers.

  The number of pull ups:

  • Anne and Bella seem to be the least sporty of Dorothy's friends; they can only do $1$ pull up.
  • Clara and Doris are able to do $3$ pull ups each.