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

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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Tuthornt

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.
$$\displaystyle\therefore\text{The mode class is}{28.5}-{33.5}$$.
$$\displaystyle\therefore{L}=\text{lower boundary point of made class}={28.5}$$
$$\displaystyle\therefore{f}_{{{1}}}=\text{frequensy of the mode class}={10}$$
$$\displaystyle\therefore{f}_{{{0}}}=\text{frequensy of the preceding class}={6}$$
$$\displaystyle\therefore{f}_{{{2}}}=\text{frequensy of the succedding class}={0}$$
$$\displaystyle\therefore{c}=\text{class length of the mode class}={5}$$
$$\displaystyle{Z}={L}+{\left({\frac{{{f}_{{{1}}}-{f}_{{{0}}}}}{{{2}\cdot{f}_{{{1}}}-{f}_{{{0}}}-{f}_{{{2}}}}}}\right)}\cdot{c}$$
$$\displaystyle={28.5}+{\left({\frac{{{10}-{6}}}{{{2}\cdot{10}-{6}-{0}}}}\right)}\cdot{5}$$
$$\displaystyle={28.5}+{\left({\frac{{{4}}}{{{14}}}}\right)}\cdot{5}$$
$$\displaystyle={28.5}+{1.4286}$$
$$\displaystyle={29.9286}$$