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Q. 1. A variable takes value x with frequency n+x –1Cx, x = 0, 1, 2, …n. The mode of the variable is.................. (1982 - 2 Marks)
Sol. Frequency for variable x is n + x –1Cx where x = 0, 1, 2, .......n.
Mode is the variable for which freq. is max.
Now, nCr is max for r = n/2, if n is even
if n is odd.
If n + x – 1 is even then for max value of n + x –1Cx,
=n –1 , ∴ freq 2n–2Cn–1
If n + x – 1 is odd then for max value of n+x-1Cx
x=n , ∴ freq 2n–1Cn
But we know 2n–1Cn =
i.e., 2n–1Cn >2n–2Cn–1
∴ Mode should be n.