Dot Plots

Dot Plots exercise

• Explain how to draw a dot plot.

  Hints

  Here you can see the first step.

  This is how the second steps looks if you want to show the frequencies of the boulders, torches, statues, and so on.

  This is a completed dot plot.

  Solution

  How can we draw a dot plot?

  1. First, draw a horizontal line.
  2. Next, label this line. Which kind of labeling you choose doesn't matter: you can choose words, or numbers, or pictures.
  3. Add the corresponding dots to show the frequency.
  4. Draw a vertical line with the labeling of the frequencies for a better understanding.
  5. You can also remove the dots up to the one showing the total frequency.

• Draw a dot plot.

  Hints

  Find the right symbol for each of the objects below the horizontal line. There is only one dot per column.

  For example, if Elz saw three apples, you would have to look for the column with the symbol of an apple and put a dot at the row with the frequency $3$.

  The solution is a composition of two words.

  Solution

  To figure out the magic word, first you have to look for the corresponding symbol below the horizontal line.

  Let's start with the boulders in the first column. Elz can see eight of them. So in the first column we count from bottom to top and mark the eighth letter, which is "B".

  In the next column we see the torches. Elz finds four of them. This gives us "E".

  Next, let's have a look at the number of statues, which is three. This leads us to "K".

  The number of skulls, five, results in "I".

  There are still two letters left:

  "N" for the one tree and "D" for the three steps.

  The magic word is "BE KIND".

• Label the dot plot.

  Hints

  If the number of roses Kyla finds is five, we have to look for the column with exactly five dots and label it with "roses".

  Solution

  Let's have a look the dot plot from left to right:

  • In the first column we find five dots, which corresponds to the number of roses.
  • The second column contains six dots, the number of lilies.
  • The third column has three dots, which represents the number of daisies.
  • The number of dots, four, in the fourth column corresponds to the number of irises.
  • The number of dots in the last column, eight, is the same as the number of asters.

• Determine how many cars of each color are passing by in one hour.

  Hints

  The total number of cars is $33$.

  You can either count the number of dots or just have a look at the vertical line.

  Solution

  Just count the number of dots in each column:

  Yellow cars - there are $7$ dots, so Kyla saw $7$ yellow cars in one hour.

  To determine the numbers of the other cars, we use the same strategy of counting dots:

  • Green cars - $6$ dots represent $6$ green cars.
  • Blue cars - $8$ dots represent $8$ blue cars.
  • Red cars - $12$ dots represent $12$ red cars.

• Find the right dot plot presenting the objects Elz can see.

  Hints

  The symbols below the horizontal line from left to the right are: boulders, torches, statues, skulls, trees, and steps.

  Check the frequency each time.

  Solution

  Here you see the right dot plot.

  To show data in a dot plot, we first draw a horizontal line and label it, for example by using pictures.

  Next, we add the number of dots corresponding to the given frequencies from left to right:

  • $8$ boulders
  • $4$ torches
  • $3$ statues
  • $5$ skulls
  • $1$ tree
  • $3$ steps

• Find the right dot plot for each data set.

  Hints

  You have to count the number of dots per column.

  You can also draw a dot plot yourself:

  • Start with the horizontal line and label it from $1$ to $6$.
  • Add the number of dots per column corresponding to the data set.
  • Compare your dot plot with the given ones.

  Solution

  Here is how you create a dot plot:

  • First, draw a horizontal line.
  • Next, label this line from left to right with $1$ to $6$.
  • Then add the number of dots which are given in each table.

  Let's start with the first table:

  $\begin{array}{l|c|c|c|c|c|c} \text{number}&1&2&3&4&5&6\\ \hline \text{frequency}&7&7&8&6&5&4 \end{array}$

  The first two columns contain $7$ dots each, the next $8$, and then $6$, $5$, and $4$ dots. The corresponding dot plot is the red one.

  In a similar way you can assign the other tables to the corresponding dot plots.

  $\begin{array}{l|c|c|c|c|c|c} \text{number}&1&2&3&4&5&6\\ \hline \text{frequency}&7&6&5&8&5&6 \end{array}$

  corresponds to the green dot plot.

  $\begin{array}{l|c|c|c|c|c|c} \text{number}&1&2&3&4&5&6\\ \hline \text{frequency}&5&6&7&8&7&6 \end{array}$

  corresponds to the yellow dot plot.

  $\begin{array}{l|c|c|c|c|c|c} \text{number}&1&2&3&4&5&6\\ \hline \text{frequency}&7&6&8&8&7&5 \end{array}$

  corresponds to the blue dot plot.