Chapter SH, Problem 4DSH

Solution

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

  $\begin{array}{c}\text{Mean}=2\\ \text{Median}=2\\ \text{Mode}=1\end{array}$

Given information:

The data set,

  $1,1,1,1,2,2,2,3,3,4$

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,

  $\begin{array}{c}\text{mean}=\frac{\left(\text{sum of items}\right)}{\left(\text{number of items}\right)}\\ =\frac{1+1+1+1+2+2+2+3+3+4}{10}\\ =\frac{20}{10}\\ =2\end{array}$

So, the mean of the given data set is $2$ .

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

  $1,1,1,1,2,2,2,3,3,4$

Since the number of items is 10, so the median is the average of the middle terms, that is

  $\begin{array}{c}\text{Median}=\frac{5^{th}\text{ term}+6^{th}\text{ term}}{2}\\ =\frac{2+2}{2}\\ =\frac{4}{2}\\ =2\end{array}$ ,

Thus, the median of the given data set is $2$ .

In order to find the mode of the given data set, note that the item 1 is repeated maximum times in the given data set, so the mode of the given data is 1.