Q14. - Algebra 1

Question

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

{111, 109, 112, 114, 119, 112}

Step-by-Step Solution

Answer

The mean of the given data is $\frac{667}{6}$, median of the given data is 112, and mode of the given data is 112.

Step 1. Write the formulae used.

• The mean of a data is: $\text{Mean}=\frac{\text{sum of all the numbers in data}}{\text{Total number of numbers in data}}$
  
• The median of a data is calculated by arranging the numbers in data in ascending order then if:

1. The numbers in the data are odd, then the median is the middle term.
2. The numbers in data are even, then the median is the average of the middle term.

• The mode of data is the most repeated number of the data. 

Step 2. Write the given information.

Numbers in data are(in ascending order): 109, 111, 112, 112, 114, 119, i.e. there are 6 numbers in data.

Step 3. DESCRIPTION OF STEP.

Use the formulae mentioned to find mean, median and mode.

$$\begin{gathered} \text{Mean}=\frac{109+111+112+112+114+119}{\text{6}} \\ =\frac{667}{6} \end{gathered}$$

Since there are 6 numbers(even) in data so the median is the average of middle terms that is 3rd and 4th numbers, that is calculated as:

$$\begin{gathered} \text{Median}=\frac{112+112}{\text{2}} \\ =112 \end{gathered}$$

Thus, the median is 112.

And it can be noticed that 112 is repeated twice and most of the time, i.e. mode of the data is 112.

 

Thus, the mean of the given data is $\frac{667}{6}$, the median of the given data is 112, and the mode of the given data is 112.