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Dots Plots Solutions

• A    dot plot    is a basic graph that uses dots or shapes to display data on a    number line    to represent each element in a data set. 

• Dot plots are useful for representing    small    data sets with countable elements. 

• Dot plots display the    frequency    of each value so the data can be visualized and compared. 
 
•    Label    the numerical scale and create a    key    for each shape on the dot plot.


Measures of center: 


•    Mean    is the average.
 
•    Median    is the middle element of the data set when the data set is ordered.
 
•    Mode    is the most frequently occurring element in the data set.


Measure of spread:
 

•    Range    is the maximum value of the data set minus the minimum value.

Note

Dot plots can sometimes be called line plots.

Example 1

Determine the mean, median, mode, and range of the dot plot.

Example 2

Construct a dot plot.

Anna asked 15 friends how many books they read in a month. She was given the following results: $\left\{3, 4, 2, 4, 5, 3, 2, 5, 5, 4, 1, 1, 3, 4, 2\right\}$  

Example 3

Construct a dot plot. Determine the mean, median, mode, and range.

Mrs. Neill’s class collected cans for a food drive. Each student collected the following number of cans:  $\left\{22, 21, 22, 24, 24, 23, 22, 20, 23, 23, 25, 26, 25, 24, 23, 24, 24, 23, 25, 24\right\}$

Mean:

$$\begin{gathered} \frac{20+21+3\left(22\right)+5\left(23\right)+6\left(24\right)+3\left(25\right)+26}{20} \\ \frac{467}{20}=23.35 \end{gathered}$$

The class collected an average of 23.35 cans per student.

Median:

$$\begin{gathered} 20, 21, 22, 22, 22, 23, 23, 23, 23,\boxed{ 23, \overline{)24},} 24, 24, 24, 24, 24, 25, 25, 25, 26 \\ \frac{23+24}{2}=23.5 \end{gathered}$$

The median is 23.5 cans.

Mode:

The mode is 24 cans.

Range:

$26–20=6$

The range is six cans.