Question

Consider the following statements:
(i) Mode can be computed from histogram

(ii) Median is not independent of change of scale
(iii) Variance is independent of change of origin and scale
Which of these is/are correct?

• A. only (i)
• B. only (ii)
• C. only (i) and (ii)
• D. (i), (ii) and (iii)

Answer 1

The correct option is C only (i) and (ii)

Mode can be computed from histogram

Median is not independent of change of scale.

Median of $1,2,3,$ is $2$

Median of $2,4,6,$ is $4$

variance depends on change of scale

If $d=\frac{x-a}{h}$ then $x=a+hd$ and $\overline{x}=a+h\overline{d}$

variance $=\frac{h^{2}f{(d-\overline{d})}^2}{N}$ where $N=\sum f^2$