Question

Find the mean of the following data using direct method :-
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Answer 1

Answer:

Given :- $\begin{tabular}{|c|c|c|c|c|c|c|}\cline{1-7}\it Class\ &\sf 0-10&\sf 10-20&\sf 20-30&\sf 30-40&\sf 40-50&\sf 50-60\\\cline{1-7}\it\ frequency (f_i)&\sf 7&\sf 5&\sf 6&\sf 12&\sf 8&\sf 2\\\cline{1-7} \end{tabular}$To Find :-Mean of the data using direct method Solution :- According to the formula $\underline{\boxed{\sf\ Mean= \dfrac{\sum f_i x_i}{\sum f_i}}}$We may prepare table $\sf\ \ 1)\ (x_i)= \dfrac{upper\ limit+\ Lower\ limit }{2}\\ \\ \sf\ \ 2)\ Calculate\ f_i x_i\ for\ each \ i$Table :- $\begin{tabular}{|c|c|c|c|}\cline{1-4}\it\underline{ Class\ Interval}&\it \underline{frequency (f_i)}&\it\underline{class\ mark (x_i)}&\it\underline{ (f_i\times x_i)}\\\cline{1-4}\sf 0-10&\sf 7 &\sf 5&\sf 35\\\sf 10-20 &\sf 5&\sf 15&\sf 75\\\sf 20-30&\sf 6&\sf 25&\sf 150\\\sf 30-40&\sf 12&\sf 35&\sf 420\\\sf 40-50&\sf 8&\sf 45&\sf 360\\\sf 50-60&\sf 2&\sf 55&\sf 110\\\cline{1-4}\cline{1-4}\sf &\it\sum f_i=40&\sf &\sf \sum(f_i\times x_i)=1150\\\cline{1-4}\end{tabular}$Now find mean $\dashrightarrow\sf\ Mean= \dfrac{\sum f_i x_i}{\sum f_i}\\ \\ \\ \dashrightarrow\sf\ Mean= \cancel{\dfrac{1150}{40}}\\ \\ \\ \dashrightarrow\boxed{\textbf{\textsf{Mean= 28.75}}}\\ \\ \\ \therefore{\underline{\sf\ Option\ (c)\ is\ the\ correct\ option}}$