Estimate the mode

A medium-sized asset management firm has 56 fund managers.  Each of these managers has its own portfolio.  The percentage returns from the managers' portfolios are shown in the table below:

Return percentage	Number of managers
0-10	8
10-20	18
20-30	21
30-40	7
40-50	2

Estimate the mode for this data set.

Correct answer:

m =  20.89

Step-by-step explanation:

$$\begin{gathered} 20\le m\le 30 \\ 8\cdot 5+18\cdot 15+21\cdot 25+7\cdot 35+2\cdot 45=m\cdot (8+18+21+7+2) \\ 56m=1170 \\ m=\frac{1170}{56}=20.89285714 \\ m=\frac{585}{28}\doteq 20.892857=20.89 \end{gathered}$$

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