If the arithmetic mean of all the terms of a table is 40 and median is 50,…

For a unimodal, moderately skewed frequency distribution, the mean, median, and mode are connected by the empirical relation Mode = 3 × Median − 2 × Mean (equivalently, Mean − Mode = 3 × (Mean − Median)).

1. Write the empirical relation connecting mean, median, and mode: Mode = 3 × Median − 2 × Mean.

2. Substitute the given mean (40) and median (50) into the relation: Mode = 3 × 50 − 2 × 40.

3. Evaluate each product: 3 × 50 = 150 and 2 × 40 = 80.

4. Subtract to obtain the mode: 150 − 80 = 70.

This can be checked using the equivalent form Mean − Mode = 3 × (Mean − Median): 40 − 70 = −30, and 3 × (40 − 50) = 3 × (−10) = −30, so both sides agree.

So the mode obtained from the given mean and median is 70, which matches the option showing that value.