The dot plot is a useful way to express numerical data. The main advantages of the dot plot are that we can find the mode and range very easily, as well as quickly see how the data is distributed. The main disadvantages are that we need to count each dot when finding the median and it is often easier to convert to a table to find the mean. The dot plot is particularly suited to data where the frequency of results are often greater than one.

In a dot plot, each dot represents one data point belonging to the result that it is placed above. The mode(s) of a dot plot will be the result(s) with the most dots. Since a dot plot stacks vertically, the greatest column(s) will belong to the mode(s).

Let's have a look at somes examples of a dot plot.

Examples

Example 1

The dot plot shows the temperature \degree \text{C} in a town over weeks. Identify the temperature that is an outlier.

A dot plot titled Temperature in a town. Ranging from 21 to 35 in steps of 1. Ask your teacher for more information.

Worked Solution

Create a strategy

Choose the value that is much greater or much smaller than the rest of the data set.

Apply the idea

\text{Outlier}=21\degree \text{C}

Example 2

A group of adults is asked: "How old were you when you passed your driving test?". The responses were: 22,\,17,\,17,\,17,\,19,\,21,\,17,\,22,\,21,\,18,\,18,\,17,\,18,\,22,\,18

The dot plot represents the responses.

A dot plot titled Responses. Ranging from 17 to 22 in steps of 1. Ask your teacher for more information.

What is the range of this data set?

Worked Solution

Create a strategy

To find the range, use the formula: \text{Range}=\text{Greatest value}-\text{Least value}

Apply the idea

\displaystyle \text{Range}	\displaystyle =	\displaystyle 22-17	Find the difference
	\displaystyle =	\displaystyle 5	Evaluate the subtraction

What is the mode of this data set?

Worked Solution

Create a strategy

Choose the value which occurs most often.

Apply the idea

\text{Mode}=17

What is the median of this data set?

Worked Solution

Create a strategy

Order the values and find the middle value.

Apply the idea

Arrange the values in order:17,\,17,\,17,\,17,\,17,\,18,\,18,\,18,\,18,\,19,\,21,\,21,\,22,\,22,\,22

Remove the smallest and largest values until you are left with one remaining value.

\text{Median}=18

How many people passed their driving test on or after their 19\text{th} birthday?

Worked Solution

Create a strategy

Count the number of dots that are greater or equal to 19.

Apply the idea

\displaystyle \text{No. People}

\displaystyle =

\displaystyle 6

Count the values

Example 3

A supermarket manager takes a note every time an employee is late to work, and how late they were (rounded to the nearest half hour). The dot plot below shows their results for the last month:

A dot plot titled Lateness (in hours). Ranging from 0 to 3 in steps of 0.5. Ask your teacher for more information.

What was the median amount of time that employees were late?

Worked Solution

Create a strategy

The median will be the mean of the two middle value in the set.

Apply the idea

List the values in order: 0.5,\,0.5,\,0.5,\,0.5,\,0.5,\,0.5,\,1,\,1,\,1,\,1,\,1,\,1.5,\\\,1.5,\,1.5,\,2,\,2,\,2,\,2.5,\,2.5,\,2.5,\,2.5,\,2.5,\,3,\,3

Remove the smallest and largest values until you are left with two remaining values.

The middle values of the set: 1.5,\,1.5

\displaystyle \text{median}	\displaystyle =	\displaystyle \dfrac{1.5+1.5}{2}	Find the mean of the middle values
	\displaystyle =	\displaystyle \dfrac{3}{2}	Evaluate the addition
	\displaystyle =	\displaystyle 1.5	Evaluate the division

\text{Median time}=1.5 \text{ hours}

What fraction of late employees were later than the median amount?

Worked Solution

Create a strategy

Count the number of dots greater than 1.5 and divide by the total number of dots.

Apply the idea

\displaystyle \text{Fraction}	\displaystyle =	\displaystyle \dfrac{3+5+2}{24}	Find the sum of the number of dots
	\displaystyle =	\displaystyle \dfrac{10}{24}	Evaluate the addition
	\displaystyle =	\displaystyle \dfrac{5}{12}	Simplify

If an employee is more than 1 hour late, the manager fines them \$10. How much money did the manager collect in fines over the last month?

Worked Solution

Create a strategy

Add the number of dots greater than 1 and multiply by the amount of the fine.

Apply the idea

\displaystyle \text{Money collected}	\displaystyle =	\displaystyle (3+3+5+2)\times 10	Add the number of dots
	\displaystyle =	\displaystyle 13 \times 10	Evaluate the addition
	\displaystyle =	\displaystyle \$130	Evaluate the multiplication

Idea summary

In a dot plot, each dot represents one data point belonging to the result that it is placed above.

The mode(s) of a dot plot will be the result(s) with the most dots. Since a dot plot stacks vertically, the greatest column(s) will belong to the mode(s).

Outcomes

6.SP.B.4

Display numerical data in plots on a number line, including dot plots, histograms, and box plots.

6.SP.B.5

Summarize numerical data sets in relation to their context, such as by:

6.SP.B.5.A

Reporting the number of observations

6.SP.B.5.B

Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.

6.SP.B.5.C

Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data was gathered.

6.SP.B.5.D

Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data was gathered

8.07 Dot plots

Ideas

Dot plots

Examples

Example 1

Example 2

Example 3

Outcomes

6.SP.B.4

6.SP.B.5

6.SP.B.5.A

6.SP.B.5.B

6.SP.B.5.C

6.SP.B.5.D

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