The mode and the rule of thumb

You will write a function for the mode of grouped data. Then you will use the rule of thumb and measure how far it is from the formula.

The idea. The mode of grouped data is $l + \dfrac{f_1 - f_0}{2f_1 - f_0 - f_2} \times h$ for the modal class. A missing neighbour has frequency $0$. The rule of thumb is $\text{mode} \approx 3 \times \text{median} - 2 \times \text{mean}$.

Your tasks.

1. In grouped_mode, return the mode of the table, rounded to $4$ decimals.
2. In estimate_mode, return the estimate of the mode from mean and median.
3. Set gap to the size of the difference between the estimate and the mode of the table below, rounded to $2$ decimals. The mean and median of this table are given.