Chapter 0.9, Problem 3E

To determine

Mean, median, and mode for the data set.

Answer to Problem 3E

Mean,

  $\overline{x}=34.4$

Median,

  $x_{\text{Med}\text{.}}=35$

Mode,

  $\left|x\right|=35$

Explanation of Solution

Given information:

Integers:

18, 35, 53, 44, 26, 57, 23, 27, 47, 33, 4, 35, 39, 41

Since there are 14 integers,

Such that

  $n=14$

Arrange them in ascending order:

4, 18, 23, 26, 27, 33, 35, 35, 39, 41, 44, 47, 53, 57

Now,

For Mean:

Mean is the usual average,

Then

Add up all the integers and divide by the number of integers.

Mean,

  $\overline{x}=\frac{{\displaystyle \sum x}}{n}=\frac{482}{14}=34.4$

For Median:

We have 14 integers.

14 is an even number.

That means

Median,

  $\begin{array}{l}{x}_{\text{Med}\text{.}}=\frac{{\left(\frac{n}{2}\right)}^{th}term+{\left(\frac{n}{2}+1\right)}^{th}term}{2}\\ =\frac{{\left(\frac{14}{2}\right)}^{th}term+{\left(\frac{14}{2}+1\right)}^{th}term}{2}\\ =\frac{7^{th}term+8^{th}term}{2}\\ =\frac{35+35}{2}\\ =35\end{array}$

For Mode:

Mode is the number which frequently occurs than any other number.

From the set of integers,

35 is the number which has occurred two times.

Thus,

Mode,

  $\left|x\right|=35$