JEE Main · 2004 · 24 Apr 2004 · Offline · Statistics

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Consider the following statements:
(a) Mode can be computed from histogram
(b) Median is not independent of change of scale
(c) Variance is independent of change of origin and scale.

Which of these is/are correct?

(A)only (a)
(B)only (b)
(C)only (a) and (b)✓ Correct
(D)(a), (b) and (c)

Answer: (C)

Solution

A histogram does let us locate the modal class and read off the mode, so the first statement is true. The median scales with the data, so it is indeed affected by a change of scale, making the second statement true. Variance is unaffected by a shift of origin but does change under a change of scale, since multiplying the data by

k

multiplies the variance by

k^{2}

, so the third statement is false. Only the first two statements are correct.

JEE Main · 2004 · 24 Apr 2004 · Offline · Single correct option

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