A) \[\operatorname{var}(ax+b)={{a}^{2}}\times \operatorname{var}(x)\]
B) SD does not get altered when every term is decreased by fixed amount.
C) SD gets altered when every term is increased by a fixed number.
D) \[CV=\frac{SD}{AM}\times 100\]
Correct Answer: C
Solution :
(c): Let every term be increased by \[k\Rightarrow {{x}_{i}}\to {{x}_{i}}+k\] Mean, \[\overline{x}\] also gets increased by \[k\Rightarrow \overline{x}\to \overline{x}+k\] \[{{(SD)}_{new}}=\sqrt{{{\left\{ {{x}_{1}}+k-\left( \overline{x}+k \right) \right\}}^{2}}+......}\] \[\sqrt{{{\left\{ \left( {{x}_{i}}+k \right)-\left( \overline{x}+k \right) \right\}}^{2}}+......}\] Naturally, k gets cancelled term by term and hence \[{{(SD)}_{new}}={{(SD)}_{old}}\]
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