The folowing table gives the frequency distribution of the sales athletic shoes

aflacatn 2021-09-11 Answered

The folowing table gives the frequency distribution of the sales athletic shoes at a store in an outlet mall cach day during the past 30 days. Calculate the mode a algebraically.
\(\begin{array}{cc}Namber of sales & Namber of days \\ 14-18 & 5 \\ 19-23 & 9 \\ 24-28 & 6 \\ 29-22 & 10\end{array}\)

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Expert Answer

Tuthornt
Answered 2021-09-12 Author has 14264 answers

Solutoins:
\(\begin{array}{|c|c|}\hline Class & Frequency(f) \\ (1) & (2) \\ \hline 14-18 & 5 \\ \hline 19-23 & 9 \\ \hline 24-28 & 6 \\ \hline 29-33 & 10 \\ \hline ... & ... \\ \hline & n=30 \\ \hline \end{array}\)
To find Mode Class
Here, maximum frequency is 10.
\(\displaystyle\therefore\text{The mode class is}{28.5}-{33.5}\).
\(\displaystyle\therefore{L}=\text{lower boundary point of made class}={28.5}\)
\(\displaystyle\therefore{f}_{{{1}}}=\text{frequensy of the mode class}={10}\)
\(\displaystyle\therefore{f}_{{{0}}}=\text{frequensy of the preceding class}={6}\)
\(\displaystyle\therefore{f}_{{{2}}}=\text{frequensy of the succedding class}={0}\)
\(\displaystyle\therefore{c}=\text{class length of the mode class}={5}\)
\(\displaystyle{Z}={L}+{\left({\frac{{{f}_{{{1}}}-{f}_{{{0}}}}}{{{2}\cdot{f}_{{{1}}}-{f}_{{{0}}}-{f}_{{{2}}}}}}\right)}\cdot{c}\)
\(\displaystyle={28.5}+{\left({\frac{{{10}-{6}}}{{{2}\cdot{10}-{6}-{0}}}}\right)}\cdot{5}\)
\(\displaystyle={28.5}+{\left({\frac{{{4}}}{{{14}}}}\right)}\cdot{5}\)
\(\displaystyle={28.5}+{1.4286}\)
\(\displaystyle={29.9286}\)

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