Chapter SH, Problem 6DSH

Solution

The mean, the median, and mode of given data set.

  $\begin{array}{c}\text{Mean}=0\\ \text{Median}=0\\ \text{Mode}=\text{None}\end{array}$

Given information:

The data set,

  $-4,-3,-2,-1,0,1,2,3,4$

Concept Used:

• Mean of a list of numbers is

$\text{mean = }\frac{\left(\text{sum of items}\right)}{\left(\text{number of items}\right)}$

• Median of a set of n numbers in numerical order is in
$\frac{n+1}{2}$ position
• Mode is the item which has greatest frequency

Calculation:

In order to find the mean of the given data set, find the sum of all the items and divide the sum by the number of items as shown below,

  $\begin{array}{c}\text{mean}=\frac{\left(\text{sum of items}\right)}{\left(\text{number of items}\right)}\\ =\frac{-4+\left(-3\right)+\left(-2\right)+\left(-1\right)+0+1+2+3+4}{9}\\ =\frac{0}{9}\\ =0\end{array}$

So, the mean of the given data set is $0$ .

Now, to find the median of the given data set, arrange the data from least to greatest first as shown below

  $-4,-3,-2,-1,0,1,2,3,4$

Since the number of items is 9, so the median is the middle terms, that is

  $\begin{array}{c}\text{Median}=\frac{9+1}{2}th\text{ term}\\ =\frac{10}{2}th\text{ term}\\ =5th\text{ term}\\ =0\end{array}$ ,

Thus, the median of the given data set is $0$ .

In order to find the mode of the given data set, note that all the items are occurring once only. So, there is no mode for the given data.