Q54. - Algebra 1

Question

Find the mean, median, and mode for each set of data.

{4,8,9,9,10,14,16}

Step-by-Step Solution

Answer

Mean = 10

Median = 9

Mode = 9

Step-1. Apply the concept of mean, median and mode.

• Mean is the average of all the observations $\text{Mean = }\frac{\text{Sum of all the observations}}{\text{Total number of observations}}$ 
• The median is the middle value when a data set is ordered from least to greatest.

• Mode is the number that occurs most often in the data set.

Step-2. Calculation of mean.

Given:

{4,8,9,9,10,14,16}

$\begin{array}{l}Mean=\frac{Sumofalltheobservations}{TotalNumberofobservations}\\ \Rightarrow Mean=\frac{4+8+9+9+10+14+16}{7}\\ \Rightarrow Mean=\frac{70}{7}=10\end{array}$

Step-3. Calculation of median.

Given:

{4,8,9,9,10,14,16}

Arrange the numbers of given set in ascending order:

4,8,9,9,10,14,16

So, the median is ${\left(\frac{7+1}{2}\right)}^{th}=4^{th}$ observation

Therefore, the median is 9

Step-4. Calculation of mode.

Given:

{4,8,9,9,10,14,16}

Arrange the numbers of given set in ascending order:

4,8,9,9,10,14,16

Since 9 occurs most often, the mode is 9.