Measures of central tendency:
Mode: The value or category that occurs with the highest frequency in a data set or distribution (the peak of the frequency curve).
Mean: The arithmetic average calculated by dividing the sum of all values by the total count.
Median: The central positional value that divides an ordered data set into two equal halves.
Range: The difference between maximum and minimum values.

Statistical distribution symmetry and outliers:
In elementary statistics tests, equality of mean and median ($\text{Mean} = \text{Median} = 20$) is taken as an indicator that the distribution is balanced with no outliers (Statement A) distorting the mean.
Mathematical Note: While equality of mean and median suggests symmetry in unimodal distributions, it does not strictly guarantee the absence of compensatory outliers (e.g., $\{2, 2, 2, 2, 20, 20, 20, 20, 20, 92\}$ has mean = median = 20). NTA officially keyed Option 1 (Only A).

Using the product rule of differentiation: $\frac{d}{dx}[u \cdot v] = u' v + u v'$
Here $u = x^2 \implies u' = 2x$
$v = \cos x \implies v' = -\sin x$

In a positively skewed (right-skewed) frequency distribution, the tail on the right side is longer or fatter. Extreme high values pull the Mean to the right more than the Median, while the Mode remains at the highest peak of the curve. Thus, the relationship is:

For symmetrical distributions: $\text{Mean} = \text{Median} = \text{Mode}$
For negatively skewed distributions: $\text{Mean} \lt \text{Median} \lt \text{Mode}$