Q10. - Algebra 1

Question

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

{62, 65, 67, 68, 73, 80, 81, 83, 99}

Step-by-Step Solution

Answer

The mean of the given data is $\frac{226}{3}$, median of the given data is 73, and there is no mode of the given data.

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): 62, 65, 67, 68, 73, 80, 81, 83, 99, i.e. there are 9 numbers in data.

Step 3. DESCRIPTION OF STEP.

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

$$\begin{gathered} \text{Mean}=\frac{62+65+67+68+73+80+81+83+99}{\text{9}} \\ =\frac{678}{9} \\ =\frac{226}{3} \end{gathered}$$

Since there are 9 numbers(odd) in data so the median is the middle term that is the 5th number, which is 73.

Thus, the median is 73.

 

And it can be noticed that no number is being repeated thus there is no mode of the given data.

 

Thus, the mean of the given data is $\frac{226}{3}$, the median of the given data is 73, and there is no mode of the given data.