Chapter B.2, Problem 10E

To determine

To calculate:

Mean, mode and median of the given data set.

Answer to Problem 10E

Mean, mode and median of the given data set is $10,10,10$ .

Explanation of Solution

Given information:

Data set: $10,2,10,19,3,7,5,3,10,31,11$

Calculation:

The average of given data set having $n$ numbers is the sum of the numbers divided by $n$ .

So mean is calculated as,

  $\begin{array}{l}\overline{x}=\frac{{\displaystyle \sum f\left(x\right)}}{n}\\ \overline{x}=\frac{10+2+10+19+3+7+5+3+10+31+11}{11}\\ \overline{x}=10.09\end{array}$

Thus, mean is $10$ .

Median of the given data set having $n$ numbers is the middle number when the numbers are written in numerical order.

If $n$ is even, the median is the average of the two middle numbers.

Now arrange given data in numerical order.

  $2,3,3,5,7,10,10,10,11,19,31$

Since $n$ is even, the median is the average of two middle numbers.

  $\begin{array}{l}=\frac{10+10}{2}\\ =10\end{array}$

Thus median is $10$ .

The mode of a data set having $n$ numbers that occurs most frequently.

So it can see that number $10$ occurs most frequently.

Thus mode is $10$ .