Chapter SH, Problem 3DSH

Solution

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

  $\begin{array}{c}\text{Mean}=3.97\\ \text{Median}=2.4\\ \text{Mode}=2.4\end{array}$

Given information:

The data set,

  $2.4,2.4,2.3,2.3,2.4,12.0$

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,

  $\begin{array}{c}\text{mean}=\frac{\left(\text{sum of items}\right)}{\left(\text{number of items}\right)}\\ =\frac{2.4+2.4+2.3+2.3+2.4+12.0}{6}\\ =\frac{23.8}{6}\\ =3.97\end{array}$

So, the mean of the given data set is $3.97$ .

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

  $\text{2}\text{.3, 2}\text{.3, 2}\text{.4, 2}\text{.4, 2}\text{.4, 12}\text{.0}$

Since the number of items is 6, so the median is the average of the middle terms, that is

  $\begin{array}{c}\text{Median}=\frac{3^{rd}\text{ terms}+4^{th}\text{ terms}}{2}\\ =\frac{2.4+2.4}{2}\\ =\frac{4.8}{2}\\ =2.4\end{array}$ ,

Thus, the median of the given data set is $2.4$ .

In order to find the mode of the given data set, note that the item $2.4$ is repeated maximum times in the given data set, so the mode of the given data is $2.4$ .