Question

Find the mode of \[10\] , \[12\], \[11\], \[10\], \[15\], \[20\],\[19\], \[21\], \[11\], \[9\], \[10\].

Answer 1

Hint: Here we will find the Mode of the given data by checking that number which is appearing most often in the series. For example, in the series \[1\], \[2\], \[2\], \[3\] and \[4\] the number \[2\] is appearing maximum times in respect of the rest numbers. So, the mode will be equals \[2\].

Complete step-by-step solution:
Step 1: First of all, we will check how many times a number is repeating itself in the series as shown below:
\[ \Rightarrow \]The number \[9\] is repeated only one time.
\[ \Rightarrow \]The number
\[10\] is repeated three times.
\[ \Rightarrow \]The number \[11\] is repeated two times.
\[ \Rightarrow \]The number \[12\] is repeated only one time.
\[ \Rightarrow \]The number \[15\] is repeated only one time.
\[ \Rightarrow \]The number \[19\] is repeated only one time.
\[ \Rightarrow \]The number \[20\] is repeated only one time.
\[ \Rightarrow \]The number \[21\] is repeated only one time.
Step 2: As we know that the mode of the series will be equal to that number that is repeating most often. So, in the above-given data the mode will be equals to as below:
\[ \Rightarrow {\text{Mode}} = 10\] \[\because \left( {{\text{because it is repeating three times}}} \right)\]

The mode will be equal to \[10\].

Note: Students should remember that if data is given with the class intervals with their respective frequency then the formula for calculating mode will be equals to as below:
\[{\text{Mode}} = l + \left( {\dfrac{{{f_1} - {f_0}}}{{2{f_1} - {f_0} - {f_2}}}} \right)h\] , where \[l\] is the lower limit of the modal class, \[h\] is the size of the class interval, \[{f_1}\] is known as the frequency of the modal class, \[{f_0}\] is known as the frequency of the class preceding the modal class, and \[{f_2}\] is known as the frequency of the class succeeding the modal class.