Question

find the mode of given data

expenditure:- 1000-1500 1500-2000 2000-2500 2500-3000
no of family:- 24 40 33 28​

Answer 1

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Answer 2

Solution :

$\begin{tabular}{|c|c|c|c|c|}\cline{1-5}\multicolumn{5}{|c|}{\bf D A T A }\\ \cline{1-5} \bf Expenditure&1000-1500&1500-2000&2000-2500&2500-3000 \\ \cline{1-5} \bf No. of family &24& 40 & 33 & 28 \\ \cline{1-5} \end{tabular}}$

$\bigstar$ Firstly, we know that formula of the mode :

$\boxed{\bf{Mode=l+\frac{f_1+f_0}{2f_1-f_0-f_2} \times h}}}$

Where as;

• Modal class = Interval with highest frequency = 1500 - 2000
• Lower limit of modal class, (l) = 1500
• Height in class Interval, (h) = 500
• Frequency of the modal class, (f1) = 40
• Frequency of class before modal class, (f0) = 24
• Frequency of class after modal class, (f2) = 33

∴ Substitute the given values :

$\longrightarrow\tt{Mode=1500+\dfrac{40+24}{2(40)-24-33} \times 500}\\\\\\\longrightarrow\tt{Mode=1500+\dfrac{64}{80-57} \times 500}\\\\\\\longrightarrow\tt{Mode=1500+\dfrac{64}{23} \times 500}\\\\\\\longrightarrow\tt{Mode=1500+\cancel{\dfrac{32000}{23} }}\\\\\\\longrightarrow\tt{Mode=1500+1391.3}\\\\\longrightarrow\bf{Mode=2891.3}$

Thus;

The mode will be 2891.3 .