Chapter SH, Problem 2DSH

Solution

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

  $\begin{array}{c}\text{Mean}=3\\ \text{Median}=3\\ \text{Mode}=3\end{array}$

Given information:

The data set,

  $0,0,1,1,2,3,3,5,3,8,7$

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,

  $\begin{array}{c}\text{mean}=\frac{\left(\text{sum of items}\right)}{\left(\text{number of items}\right)}\\ =\frac{0+0+1+1+2+3+3+5+3+8+7}{11}\\ =\frac{33}{11}\\ =3\end{array}$

So, the mean of the given data set is $3$ .

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

  $\text{0, 0, 1, 1, 2, 3, 3, 3, 5, 7, 8}$

Since the number of items is 11, so the median is

  $\begin{array}{c}\frac{n+1}{2}=\frac{11+1}{2}\\ =\frac{12}{2}\\ =6\end{array}$ ,

Thus, the median is in 6^th position, that is, the median is 3.

In order to find the mode of the given data set, note that the item 3 is repeated maximum times in the given data set, so the mode of the given data is 3.