The dot plot tells us the following:

• there is $\color{blue}1$ value in the data set equal to $10$

• there is $\color{blue}1$ value in the data set equal to $20$

• tthere are $\color{blue}2$ values in the data set equal to $30$

• there is $\color{blue}1$ value in the data set equal to $40$

So, we get the following data:

\[ 10, \: 20, \: 30, \: 30, \: 40 \]

Finally, we calculate the mean: \begin{align*} \text{mean} &= \dfrac{(10 \times {\color{blue}1}) + (20 \times {\color{blue}1}) + (30 \times {\color{blue}2}) + (40\times {\color{blue}1})}{5} \\[2pt] &= \dfrac{10 + 20 + 60 + 40}{5} \\[2pt] &= \dfrac{130}{5} \\[2pt] &= 26 \end{align*}

Therefore, the mean of the distribution is $26.$

The dot plot tells us the following:

• $\color{blue}1$ student is $10$ years old

• $\color{blue}3$ students are $12$ years old

• $\color{blue}2$ students are $13$ years old

So, we get the following data:

\[ 10, \: 12, \: 12, \: 12, \: 13, \: 13 \]

Finally, we calculate the mean: \begin{align*} \text{mean} &= \dfrac{(10 \times {\color{blue}1}) + (12 \times {\color{blue}3}) + (13 \times {\color{blue}2})}{6} \\[5pt] &= \dfrac{10 + 36 + 26}{6} \\[5pt] &= \dfrac{72}{6} \\[5pt] &= 12 \end{align*}

Therefore, the mean age of the students is $12.$

The mode is the value that occurs most often in the data set.

According to our plot, the value $\color{blue}5$ appears more frequently than the others ($\color{red}4$ times in total).

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\[\]

Therefore, the mode is $5.$

The mode is the value that occurs most often in the data set.

According to our plot, the value $\color{blue}10$ appears more frequently than the others ($\color{red}4$ times in total).

\[\]

\[\]

Therefore, the mode is $10.$

Method 1

Since we have an odd number of data points ($5$ in total), the median is the middle value ($\color{blue}3$rd).

Therefore, the median is $\color{blue}21$ years old.

Method 2

The dot plot tells us the following:

• $\color{blue}2$ employees are $19$ years old

• $\color{blue}2$ employees are $21$ years old

• $\color{blue}1$ employee is $23$ years old

This gives the following data: \[ 19, \: 19, \: {\color{blue}\underline{21}}, \: 21, \: 23 \] Since we have an odd number of data points ($5$ in total), the median is the middle value ($\color{blue}3$rd).

Therefore, the median age is $21$ years old.

Method 1

Since we have an even number of data points ($16$ in total), the median is the mean of the two middle values ($\color{blue}8$th and $\color{blue}9$th, respectively).

Therefore, the median is \[ \text{median} = \dfrac{{\color{blue}5} + {\color{blue}7}}{2} = \dfrac{12}{2} = 6. \]

Method 2

The dot plot tells us the following:

• $\color{blue}3$ vehicles consumed $4$ liters

• $\color{blue}5$ vehicles consumed $5$ liters

• $\color{blue}5$ vehicles consumed $7$ liters

• $\color{blue}3$ vehicles consumed $8$ liters

This gives the following data: \[ 4, \: 4, \: 4, \: 5, \: 5, \: 5, \: 5, \: {\color{blue}\underline{5}}, \: {\color{blue}\underline{7}}, \: 7, \: 7, \: 7, \: 7, \: 8, \: 8, \: 8 \] Since we have an even number of data points ($16$ in total), the median is the mean of the two middle values ($\color{blue}8$th and $\color{blue}9$th, respectively).

Therefore, the median is \[ \text{median} = \dfrac{{\color{blue}5} + {\color{blue}7}}{2} = \dfrac{12}{2} = 6. \]