Q49. - Algebra 1

Question

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

$\left\{7,6,5,7,4,8,2,2,7,8\right\}$

Step-by-Step Solution

Answer

The mean, median, and mode of the set of data $\mathbf{\{}\mathbf{7}\mathbf{,}\mathbf{6}\mathbf{,}\mathbf{5}\mathbf{,}\mathbf{7}\mathbf{,}\mathbf{4}\mathbf{,}\mathbf{8}\mathbf{,}\mathbf{2}\mathbf{,}\mathbf{2}\mathbf{,}\mathbf{7}\mathbf{,}\mathbf{8}\mathbf{\}}$ are 5.6, 6.5, and 7 respectively.

Step 1. Define mean, median, mode.

The mean of a set of data is the quotient of the sum of observations and the number of observations.

The median is the middle number in a sorted, ascending, or descending, set of numbers.

The mode of the set of data is the observation that occurs highest times.

Step 2. Calculate mean.

The sum of observation for the given set of data is:  

$7+6+5+7+4+8+2+2+7+8=56$

And, the total number of observations is 10. 

So, the mean of the given set of data is $\frac{56}{10}=5.6$.

Step 3. Calculate median.

The given set of data in ascending order is $\left\{2,2,4,5,6,7,7,7,8,8\right\}$. The total number of observations is 10, i.e., even.

The median of the set of data is the mean of the fifth and sixth observations.

$\begin{array}{c}\frac{5+6}{2}=\frac{13}{2}\\ =6.5\end{array}$

So, the median of the given set of data is 6.5.

Step 4. Calculate mode.

In the given data set, observation 7 in the set occurs most of the time. So, the mode of the given set of data is 7.

Therefore, the mean, median, and mode of the set of data $\{7,6,5,7,4,8,2,2,7,8\}$ are 5.6, 6.5, and 7 respectively.